travel speed definition

Speed and Velocity

What's the difference between two identical objects traveling at different speeds? Nearly everyone knows that the one moving faster (the one with the greater speed) will go farther than the one moving slower in the same amount of time. Either that or they'll tell you that the one moving faster will get where it's going sooner than the slower one. Whatever speed is, it involves both distance and time. "Faster" means either "farther" (greater distance) or "sooner" (less time).

Doubling one's speed would mean doubling one's distance traveled in a given amount of time. Doubling one's speed would also mean halving the time required to travel a given distance. If you know a little about mathematics, these statements are meaningful and useful. (The symbol v is used for speed because of the association between speed and velocity, which will be discussed shortly.)

• Speed is directly proportional to distance when time is constant: v  ∝  s ( t  constant)
• Speed is inversely proportional to time when distance is constant: v  ∝  1 t ( s  constant)

Combining these two rules together gives the definition of speed in symbolic form.

Don't like symbols? Well then, here's another way to define speed. Speed is the rate of change of distance with time.

In order to calculate the speed of an object we must know how far it's gone and how long it took to get there. "Farther" and "sooner" correspond to "faster". Let's say you drove a car from New York to Boston. The distance by road is roughly 300 km (200 miles). If the trip takes four hours, what was your speed? Applying the formula above gives…

This is the answer the equation gives us, but how right is it? Was 75 kph the speed of the car? Yes, of course it was… Well, maybe, I guess… No, it couldn't have been the speed. Unless you live in a world where cars have some kind of exceptional cruise control and traffic flows in some ideal manner, your speed during this hypothetical journey must certainly have varied. Thus, the number calculated above is not the speed of the car, it's the average speed for the entire journey. In order to emphasize this point, the equation is sometimes modified as follows…

The bar over the v indicates an average or a mean and the ∆ (delta) symbol indicates a change. Read it as "vee bar is delta ess over delta tee". This is the quantity we calculated for our hypothetical trip.

In contrast, a car's speedometer shows its instantaneous speed , that is, the speed determined over a very small interval of time — an instant. Ideally this interval should be as close to zero as possible, but in reality we are limited by the sensitivity of our measuring devices. Mentally, however, it is possible to imagine calculating average speed over ever smaller time intervals until we have effectively calculated instantaneous speed. This idea is written symbolically as…

or, in the language of calculus speed is the first derivative of distance with respect to time.

If you haven't dealt with calculus, don't sweat this definition too much. There are other, simpler ways to find the instantaneous speed of a moving object. On a distance-time graph, speed corresponds to slope and thus the instantaneous speed of an object with non-constant speed can be found from the slope of a line tangent to its curve. We'll deal with that later in this book.

In order to calculate the speed of an object we need to know how far it's gone and how long it took to get there. A wise person would then ask…

What do you mean by how far ? Do you want the distance or the displacement ? A wise person, once upon a time

Your choice of answer to this question determines what you calculate — speed or velocity.

• Average speed is the rate of change of distance with time.
• Average velocity is the rate of change of displacement with time.

And for the calculus people out there…

• Instantaneous speed is the first derivative of distance with respect to time.
• Instantaneous velocity is the first derivative of displacement with respect to time.

Speed and velocity are related in much the same way that distance and displacement are related. Speed is a scalar and velocity is a vector. Speed gets the symbol v (italic) and velocity gets the symbol v (boldface). Average values get a bar over the symbol.

Displacement is measured along the shortest path between two points and its magnitude is always less than or equal to the distance. The magnitude of displacement approaches distance as distance approaches zero. That is, distance and displacement are effectively the same (have the same magnitude) when the interval examined is "small". Since speed is based on distance and velocity is based on displacement, these two quantities are effectively the same (have the same magnitude) when the time interval is "small" or, in the language of calculus, the magnitude of an object's average velocity approaches its average speed as the time interval approaches zero.

The instantaneous speed of an object is then the magnitude of its instantaneous velocity.

v  = | v |

Speed tells you how fast. Velocity tells you how fast and in what direction.

Speed and velocity are both measured using the same units. The SI unit of distance and displacement is the meter. The SI unit of time is the second. The SI unit of speed and velocity is the ratio of two — the meter per second .

This unit is only rarely used outside scientific and academic circles. Most people on this planet measure speeds in kilometer per hour (km/h or kph). The United States is an exception in that we use the older mile per hour (mi/h or mph). Let's determine the conversion factors so that we can relate speeds measured in m/s with the more familiar units.

The decimal values shown above are accurate to four significant digits, but the fractional values should only be considered rules of thumb (1 kph is really more like 2 7  m/s than 1 4  m/s and 1 mph is more like 4 9  m/s than 1 2  m/s).

The ratio of any unit of distance to any unit of time is a unit of speed.

• The speeds of ships, planes, and rockets are often stated in knots . One knot is one nautical mile per hour — a nautical mile being 1,852 m or 6,076 feet and an hour being 3,600 s. NASA still reports the speed of its rockets in knots and their downrange distance in nautical miles. One knot is approximately 0.5144 m/s.
• The slowest speeds are measured over the longest time periods. The continental plates creep across the surface of the Earth at the geologically slow rate of 1–10  cm/year or 1–10  m/century — about the same speed that fingernails and hair grow.
• Audio cassette tape travels at 1⅞ inches per second (ips). When magnetic tape was first invented, it was spooled on to open reels like movie film. These early reel-to-reel tape recorders ran the tape through at 15 ips. Later models could also record at half this speed (7½ ips) and then half of that (3¾ ips) and then some at half of that (1⅞ ips). When the audio cassette standard was being formulated, it was decided that the last of these values would be sufficient for the new medium. One inch per second is exactly 0.0254 m/s by definition.

Sometimes, the speed of an object is described relative to the speed of something else; preferably some physical phenomenon.

• Aerodynamics is the study of moving air and how objects interact with it. In this field, the speed of an object is often measured relative to the speed of sound . This ratio is known as the Mach number . The speed of sound is roughly 295 m/s (660 mph) at the altitude at which commercial jet aircraft normally fly. The now decommissioned British Airways and Air France supersonic Concorde cruised at 600 m/s (1,340 mph). Simple division shows that this speed is roughly twice the speed of sound or Mach 2.0, which is exceptionally fast. A Boeing 777, in comparison, cruises at 248 m/s (555 mph) or Mach 0.8, which only seems slow in comparison to the Concorde.
• The speed of light in a vacuum is defined in the SI system to be 299,792,458 m/s (about a billion km/h). This is usually stated with a more reasonable precision as 3.00 × 10 8  m/s. The speed of light in a vacuum is assigned the symbol c (italic) when used in an equation and c (roman) when used as a unit. The speed of light in a vacuum is a universal limit, so real objects always move slower than c . It is used frequently in particle physics and the astronomy of distant objects. The most distant observed objects are quasars; short for "quasi-stellar radio objects". They are visually similar to stars (the prefix quasi means resembling) but emit far more energy than any star possibly could. They lie at the edges of the observable universe and are rushing away from us at incredible speeds. The most distant quasars are moving away from us at nearly 0.9 c. By the way, the symbol c was chosen not because the speed of light is a universal constant (which it is) but because it is the first letter of the Latin word for swiftness — celeritas .

What Speed Actually Means in Physics

• Physics Laws, Concepts, and Principles
• Quantum Physics
• Important Physicists
• Thermodynamics
• Cosmology & Astrophysics
• Weather & Climate

• M.S., Mathematics Education, Indiana University
• B.A., Physics, Wabash College

Speed is the distance traveled per unit of time. It is how fast an object is moving. Speed is the scalar quantity that is the magnitude of the velocity vector. It doesn't have a direction. Higher speed means an object is moving faster. Lower speed means it is moving slower. If it isn't moving at all, it has zero speed.

The most common way to calculate the constant velocity of an object moving in a straight line is the formula:

r = d / t

• r is the rate, or speed (sometimes denoted as v , for velocity )
• d is the distance moved
• t is the time it takes to complete the movement

This equation gives the average speed of an object over an interval of time. The object may have been going faster or slower at different points during the time interval, but we see here its average speed.

The instantaneous speed is the limit of the average speed as the time interval approaches zero. When you look at a speedometer in a car, you are seeing the instantaneous speed. While you may have been going 60 miles per hour for a moment, your average rate of speed for ten minutes might be far more or far less.

Units for Speed

The SI units for speed are m/s (meters per second). In everyday usage, kilometers per hour or miles per hour are the common units of speed. At sea, knots (or nautical miles) per hour is a common speed. 

Conversions for Unit of Speed

Speed vs velocity.

Speed is a scalar quantity, it does not account for direction, while velocity is a vector quantity which is aware of direction. If ran across the room and then returned to your original position, you would have a speed — the distance divided by the time. But your velocity would be zero since your position didn't change between the beginning and the end of the interval. There was no displacement seen at the end of the time period. You would have an instantaneous velocity if it were taken at a point where you had moved from your original position. If you go two steps forward and one step back, your speed isn't affected, but your velocity would be.

Rotational Speed and Tangential Speed

Rotational speed, or angular speed, is the number of revolutions over a unit of time for an object traveling in a circular path. Revolutions per minute (rpm) is a common unit. But how far from the axis an object is its radial distance as it revolves determines its tangential speed, which is the linear speed of an object on a circular path?

At one rpm, a point that is at the edge of a record disk is covering more distance in a second than a point closer to the center. At the center, the tangential speed is zero. Your tangential speed is proportional to the radial distance times the rate of rotation.

Tangential speed = radial distance x rotational speed.

• Can Anything Move Faster Than the Speed of Light?
• Understanding the Heisenberg Uncertainty Principle
• Einstein's Theory of Relativity
• Does Time Really Exist?
• What Is the Twin Paradox? Real Time Travel
• Quantum Entanglement in Physics
• What Is Time? A Simple Explanation
• Everything You Need to Know About Bell's Theorem
• The Discovery of the Higgs Energy Field
• Science Comic Books
• Introduction to the Major Laws of Physics
• Neutrinos in Particle Physics
• Life of Léon Foucault, Physicist Who Measured the Speed of Light
• Is Time Travel Possible?
• What Is Velocity in Physics?
• Understanding Cosmology and Its Impact

What is speed in physics? (Definition, Formula, and Examples)

• February 28, 2022
• Kinematics , Mechanics

Concept of speed is one of the first concepts when we start studying physics. The concept of speed is discussed under kinematics. In this article, we will learn about the concept of speed, its formula, unit along with some examples. Let us first begin by defining speed.

Table of Contents

Definition of Speed In Physics

The distance travelled per unit of time is referred to as speed. It is the rate at which a body moves.

Speed is a scalar quantity that is nothing but the magnitude of the velocity vector. Since speed is a scalar quantity it only has magnitude but no direction.

It must be noted that

• A higher speed indicates that an object is travelling fast.
• If the object is travelling slowly then it has a lesser speed.
• Object under consideration has 0 speed if it is not moving at all.

See Also: Difference between Speed and Velocity

Formula for speed

In order to calculate speed, you divide the distance traveled by the amount of time it took you to cover that distance.

If s is the speed of the object and d is the distance covered by that object in time t then the formula for speed is given by the relation

$$s=\frac{d}{t}$$

The above equation computes an object’s average speed over time. During its course of motion, the object may have been going faster or slower at different points of time during the given time interval. What we see here is the average speed of the object.

See Also: Distance and Displacement

Unit of Speed

In the SI system of units, speed is measured in meters per second (m/s) (meters per second). In general day-to-day usage, the units of speed are kilometers per hour or miles per hour.

In the CGS system of units speed is measured in centimeters per second (cm/s).

Types of Speed

There are four types of speed and they are:

• Uniform speed:- When an object travels the same distance in the same time intervals, it is said to be moving at a uniform speed.
• Non-Uniform or variable speed:- Non-uniform speed occurs when an object covers a unequal distance at equal intervals of time.
• Average speed:- The average speed of a body over a certain time interval is equal to the distance travelled by the body divided by the time.
• Instantaneous speed :- The instantaneous speed of a particle is the speed of the particle at any instant of time or at any point on its path. It tells us about how fast an object is moving anywhere along its path. When you look at a speedometer in a car, you are seeing the instantaneous speed of the car.

Measurement of Speed

Speedometers are used in automobiles to measure speed. Odometers are used to track the distance traveled.

While solving problems in graphs can also be used to calculate speed. The Position-time graph aids in understanding an object’s speed. We can find average velocity on a position-time graph . Apart from this, we can also use a position-time graph for finding instantaneous velocity .

Examples of Speed

Let us now look at some examples of speed.

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2.2 Speed and Velocity

Section learning objectives.

By the end of this section, you will be able to do the following:

• Calculate the average speed of an object
• Relate displacement and average velocity

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (B) describe and analyze motion in one dimension using equations with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, and acceleration.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Position and Speed of an Object, as well as the following standards:

Section Key Terms

In this section, students will apply what they have learned about distance and displacement to the concepts of speed and velocity.

[BL] [OL] Before students read the section, ask them to give examples of ways they have heard the word speed used. Then ask them if they have heard the word velocity used. Explain that these words are often used interchangeably in everyday life, but their scientific definitions are different. Tell students that they will learn about these differences as they read the section.

[AL] Explain to students that velocity, like displacement, is a vector quantity. Ask them to speculate about ways that speed is different from velocity. After they share their ideas, follow up with questions that deepen their thought process, such as: Why do you think that? What is an example? How might apply these terms to motion that you see every day?

There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we will look at time , speed, and velocity to expand our understanding of motion.

A description of how fast or slow an object moves is its speed. Speed is the rate at which an object changes its location. Like distance, speed is a scalar because it has a magnitude but not a direction. Because speed is a rate, it depends on the time interval of motion. You can calculate the elapsed time or the change in time, Δ t Δ t , of motion as the difference between the ending time and the beginning time

The SI unit of time is the second (s), and the SI unit of speed is meters per second (m/s), but sometimes kilometers per hour (km/h), miles per hour (mph) or other units of speed are used.

When you describe an object's speed, you often describe the average over a time period. Average speed , v avg , is the distance traveled divided by the time during which the motion occurs.

You can, of course, rearrange the equation to solve for either distance or time

Suppose, for example, a car travels 150 kilometers in 3.2 hours. Its average speed for the trip is

A car's speed would likely increase and decrease many times over a 3.2 hour trip. Its speed at a specific instant in time, however, is its instantaneous speed . A car's speedometer describes its instantaneous speed.

[OL] [AL] Caution students that average speed is not always the average of an object's initial and final speeds. For example, suppose a car travels a distance of 100 km. The first 50 km it travels 30 km/h and the second 50 km it travels at 60 km/h. Its average speed would be distance /(time interval) = (100 km)/[(50 km)/(30 km/h) + (50 km)/(60 km/h)] = 40 km/h. If the car had spent equal times at 30 km and 60 km rather than equal distances at these speeds, its average speed would have been 45 km/h.

[BL] [OL] Caution students that the terms speed, average speed, and instantaneous speed are all often referred to simply as speed in everyday language. Emphasize the importance in science to use correct terminology to avoid confusion and to properly communicate ideas.

Worked Example

Calculating average speed.

A marble rolls 5.2 m in 1.8 s. What was the marble's average speed?

We know the distance the marble travels, 5.2 m, and the time interval, 1.8 s. We can use these values in the average speed equation.

Average speed is a scalar, so we do not include direction in the answer. We can check the reasonableness of the answer by estimating: 5 meters divided by 2 seconds is 2.5 m/s. Since 2.5 m/s is close to 2.9 m/s, the answer is reasonable. This is about the speed of a brisk walk, so it also makes sense.

Practice Problems

A pitcher throws a baseball from the pitcher’s mound to home plate in 0.46 s. The distance is 18.4 m. What was the average speed of the baseball?

The vector version of speed is velocity. Velocity describes the speed and direction of an object. As with speed, it is useful to describe either the average velocity over a time period or the velocity at a specific moment. Average velocity is displacement divided by the time over which the displacement occurs.

Velocity, like speed, has SI units of meters per second (m/s), but because it is a vector, you must also include a direction. Furthermore, the variable v for velocity is bold because it is a vector, which is in contrast to the variable v for speed which is italicized because it is a scalar quantity.

Tips For Success

It is important to keep in mind that the average speed is not the same thing as the average velocity without its direction. Like we saw with displacement and distance in the last section, changes in direction over a time interval have a bigger effect on speed and velocity.

Suppose a passenger moved toward the back of a plane with an average velocity of –4 m/s. We cannot tell from the average velocity whether the passenger stopped momentarily or backed up before he got to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals such as those shown in Figure 2.9 . If you consider infinitesimally small intervals, you can define instantaneous velocity , which is the velocity at a specific instant in time. Instantaneous velocity and average velocity are the same if the velocity is constant.

Earlier, you have read that distance traveled can be different than the magnitude of displacement. In the same way, speed can be different than the magnitude of velocity. For example, you drive to a store and return home in half an hour. If your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero because your displacement for the round trip is zero.

Watch Physics

Calculating average velocity or speed.

This video reviews vectors and scalars and describes how to calculate average velocity and average speed when you know displacement and change in time. The video also reviews how to convert km/h to m/s.

• A scalar quantity is fully described by its magnitude, while a vector needs both magnitude and direction to fully describe it. Displacement is an example of a scalar quantity and time is an example of a vector quantity.
• A scalar quantity is fully described by its magnitude, while a vector needs both magnitude and direction to fully describe it. Time is an example of a scalar quantity and displacement is an example of a vector quantity.
• A scalar quantity is fully described by its magnitude and direction, while a vector needs only magnitude to fully describe it. Displacement is an example of a scalar quantity and time is an example of a vector quantity.
• A scalar quantity is fully described by its magnitude and direction, while a vector needs only magnitude to fully describe it. Time is an example of a scalar quantity and displacement is an example of a vector quantity.

This video does a good job of reinforcing the difference between vectors and scalars. The student is introduced to the idea of using ‘s’ to denote displacement, which you may or may not wish to encourage. Before students watch the video, point out that the instructor uses s → s → for displacement instead of d, as used in this text. Explain the use of small arrows over variables is a common way to denote vectors in higher-level physics courses. Caution students that the customary abbreviations for hour and seconds are not used in this video. Remind students that in their own work they should use the abbreviations h for hour and s for seconds.

Calculating Average Velocity

A student has a displacement of 304 m north in 180 s. What was the student's average velocity?

We know that the displacement is 304 m north and the time is 180 s. We can use the formula for average velocity to solve the problem.

Since average velocity is a vector quantity, you must include direction as well as magnitude in the answer. Notice, however, that the direction can be omitted until the end to avoid cluttering the problem. Pay attention to the significant figures in the problem. The distance 304 m has three significant figures, but the time interval 180 s has only two, so the quotient should have only two significant figures.

Note the way scalars and vectors are represented. In this book d represents distance and displacement. Similarly, v represents speed, and v represents velocity. A variable that is not bold indicates a scalar quantity, and a bold variable indicates a vector quantity. Vectors are sometimes represented by small arrows above the variable.

Use this problem to emphasize the importance of using the correct number of significant figures in calculations. Some students have a tendency to include many digits in their final calculations. They incorrectly believe they are improving the accuracy of their answer by writing many of the digits shown on the calculator. Point out that doing this introduces errors into the calculations. In more complicated calculations, these errors can propagate and cause the final answer to be wrong. Instead, remind students to always carry one or two extra digits in intermediate calculations and to round the final answer to the correct number of significant figures.

Solving for Displacement when Average Velocity and Time are Known

Layla jogs with an average velocity of 2.4 m/s east. What is her displacement after 46 seconds?

We know that Layla's average velocity is 2.4 m/s east, and the time interval is 46 seconds. We can rearrange the average velocity formula to solve for the displacement.

The answer is about 110 m east, which is a reasonable displacement for slightly less than a minute of jogging. A calculator shows the answer as 110.4 m. We chose to write the answer using scientific notation because we wanted to make it clear that we only used two significant figures.

Dimensional analysis is a good way to determine whether you solved a problem correctly. Write the calculation using only units to be sure they match on opposite sides of the equal mark. In the worked example, you have m = (m/s)(s). Since seconds is in the denominator for the average velocity and in the numerator for the time, the unit cancels out leaving only m and, of course, m = m.

Solving for Time when Displacement and Average Velocity are Known

Phillip walks along a straight path from his house to his school. How long will it take him to get to school if he walks 428 m west with an average velocity of 1.7 m/s west?

We know that Phillip's displacement is 428 m west, and his average velocity is 1.7 m/s west. We can calculate the time required for the trip by rearranging the average velocity equation.

Here again we had to use scientific notation because the answer could only have two significant figures. Since time is a scalar, the answer includes only a magnitude and not a direction.

• 4 km/h north
• 4 km/h south
• 64 km/h north
• 64 km/h south

A bird flies with an average velocity of 7.5 m/s east from one branch to another in 2.4 s. It then pauses before flying with an average velocity of 6.8 m/s east for 3.5 s to another branch. What is the bird’s total displacement from its starting point?

Virtual Physics

The walking man.

In this simulation you will put your cursor on the man and move him first in one direction and then in the opposite direction. Keep the Introduction tab active. You can use the Charts tab after you learn about graphing motion later in this chapter. Carefully watch the sign of the numbers in the position and velocity boxes. Ignore the acceleration box for now. See if you can make the man’s position positive while the velocity is negative. Then see if you can do the opposite.

Grasp Check

Which situation correctly describes when the moving man’s position was negative but his velocity was positive?

• Man moving toward 0 from left of 0
• Man moving toward 0 from right of 0
• Man moving away from 0 from left of 0
• Man moving away from 0 from right of 0

This is a powerful interactive animation, and it can be used for many lessons. At this point it can be used to show that displacement can be either positive or negative. It can also show that when displacement is negative, velocity can be either positive or negative. Later it can be used to show that velocity and acceleration can have different signs. It is strongly suggested that you keep students on the Introduction tab. The Charts tab can be used after students learn about graphing motion later in this chapter.

Check Your Understanding

• Yes, because average velocity depends on the net or total displacement.
• Yes, because average velocity depends on the total distance traveled.
• No, because the velocities of both runners must remain exactly the same throughout the journey.
• No, because the instantaneous velocities of the runners must remain the same at the midpoint but can vary at other points.

If you divide the total distance traveled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity, and under what circumstances are these two quantities the same?

• Average speed. Both are the same when the car is traveling at a constant speed and changing direction.
• Average speed. Both are the same when the speed is constant and the car does not change its direction.
• Magnitude of average velocity. Both are same when the car is traveling at a constant speed.
• Magnitude of average velocity. Both are same when the car does not change its direction.
• Yes, if net displacement is negative.
• Yes, if the object’s direction changes during motion.
• No, because average velocity describes only the magnitude and not the direction of motion.
• No, because average velocity only describes the magnitude in the positive direction of motion.

Use the Check Your Understanding questions to assess students’ achievement of the sections learning objectives. If students are struggling with a specific objective, the Check Your Understanding will help identify which and direct students to the relevant content. Assessment items in TUTOR will allow you to reassess.

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Speed and Velocity with Examples

In the last sections we have learned scalar and vector concepts. Beyond the definitions of these concepts we will try to explain speed and velocity terms. As mentioned in last section distance and displacement are different terms. Distance is a scalar quantity and displacement is a vector quantity. In the same way we can categorize speed and velocity. Speed is a scalar quantity with just concerning the magnitude and velocity is a vector quantity that must consider both magnitude and direction.

From the above formula we can say that speed is directly proportional to the distance and inversely proportional to the time. I think it’s time to talk a little bit the units of speed. Motor vehicles commonly use kilometer per hour (km/h) as a unit of speed however in short distances we can use meter per second (m/s) as a unit of speed. In my examples and explanations I will use m/s as a unit.

Example: Calculate the speed of the car that travels 450m in 9 seconds. Speed = Distance / Time Speed = 450m / 9 s = 50 m/s

Total distance covered = 45m + 6m = 81m

Speed = total distance/time of travel = 81m / 27s = 3m/s

Velocity = displacement/time = (45-36) m / 27s = 9m /27s = 0,33m/s

We show with this example that speed and velocity are not the same thing.

Average Speed and Instantaneous Speed

Average Velocity and Instantaneous Velocity

Average Velocity=Displacement/Time Interval Displacement =150m-70m=80m

Average Velocity= 80m/10s=8m/s east

Average Speed=Total Distance Traveled/Time Interval

Average Speed= (150m+70m)/10s

Average Speed=22m/s

This is a good example which shows the difference of velocity and speed clearly. We must give the direction with velocity since velocity is a vector quantity however, speed is a scalar quantity and we do not consider direction.

Kinematics Exams and Solutions

Speed and Velocity

Speed is how fast something moves.

Velocity is speed with a direction .

Saying Ariel the Dog runs at 9 km/h (kilometers per hour) is a speed.

But saying he runs 9 km/h Westwards is a velocity.

Imagine something moving back and forth very fast: it has a high speed, but a low (or zero) velocity.

Speed is measured as distance moved over time.

Speed = Distance Time

Example: A car travels 50 km in one hour.

Its average speed is 50 km per hour (50 km/h)

Speed = Distance Time = 50 km 1 hour

We can also use these symbols:

Speed = Δs Δt

Where Δ (" Delta ") means "change in", and

• s means distance ("s" for "space")
• t means time

Example: You run 360 m in 60 seconds.

So your speed is 6 meters per second (6 m/s).

Speed is commonly measured in:

• meters per second (m/s or m s -1 ), or
• kilometers per hour (km/h or km h -1 )

A km is 1000 m, and there are 3600 seconds in an hour, so we can convert like this (see Unit Conversion Method to learn more):

So 1 m/s is equal to 3.6 km/h

Example: What is 20 m/s in km/h ?

20 m/s × 3.6 km/h 1 m/s = 72 km/h

Example: What is 120 km/h in m/s ?

120 km/h × 1 m/s 3.6 km/h = 33.333... m/s

Average vs Instantaneous Speed

The examples so far calculate average speed : how far something travels over a period of time.

But speed can change as time goes by. A car can go faster and slower, maybe even stop at lights.

So there is also instantaneous speed : the speed at an instant in time. We can try to measure it by using a very short span of time (the shorter the better).

Example: Sam uses a stopwatch and measures 1.6 seconds as the car travels between two posts 20 m apart. What is the instantaneous speed ?

Well, we don't know exactly, as the car may have been speeding up or slowing down during that time, but we can estimate:

20 m 1.6 s = 12.5 m/s = 45 km/h

It is really still an average, but is close to an instantaneous speed.

Constant Speed

When the speed does not change it is constant .

For constant speed, the average and instantaneous speeds are the same.

Because the direction is important velocity uses displacement instead of distance:

Velocity = Displacement Time in a direction.

Example: You walk from home to the shop in 100 seconds, what is your speed and what is your velocity?

Speed = 220 m 100 s = 2.2 m/s

Velocity = 130 m 100 s East = 1.3 m/s East

You forgot your money so you turn around and go back home in 120 more seconds: what is your round-trip speed and velocity?

The total time is 100 s + 120 s = 220 s:

Speed = 440 m 220 s = 2.0 m/s

Velocity = 0 m 220 s = 0 m/s

Yes, the velocity is zero as you ended up where you started.

Learn more at Vectors .

Motion is relative. When we say something is "at rest" or "moving at 4 m/s" we forget to say "in relation to me" or "in relation to the ground", etc.

Think about this: are you really standing still? You are on planet Earth which is spinning at 40,075 km per day (about 1675 km/h or 465 m/s), and moving around the Sun at about 100,000 km/h, which is itself moving through the Galaxy.

Next time you are out walking, imagine you are still and it is the world that moves under your feet. Feels great.

It is all relative!

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Speed, Distance, and Time

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A common set of physics problems ask students to determine either the speed, distance, or travel time of something given the other two variables. These problems are interesting since they describe very basic situations that occur regularly for many people. For example, a problem might say: "Find the distance a car has traveled in fifteen minutes if it travels at a constant speed of \(75 \text {km/hr}\)." Often in these problems, we work with an average velocity or speed, which simplifies the laws of motion used to calculate the desired quantity. Let's see how that works.

Application and Extensions

As long as the speed is constant or average, the relationship between speed , distance , and time is expressed in this equation

\[\mbox{Speed} = \frac{\mbox{Distance}}{\mbox{Time}},\]

which can also be rearranged as

\[\mbox{Time} = \frac{\mbox{Distance}}{\mbox{Speed}}\]

\[\mbox{Distance} = \mbox{Speed} \times \mbox{Time}.\]

Speed, distance, and time problems ask to solve for one of the three variables given certain information. In these problems, objects are moving at either constant speeds or average speeds.

Most problems will give values for two variables and ask for the third.

Bernie boards a train at 1:00 PM and gets off at 5:00 PM. During this trip, the train traveled 360 kilometers. What was the train's average speed in kilometers per hour? In this problem, the total time is 4 hours and the total distance is \(360\text{ km},\) which we can plug into the equation: \[\mbox{Speed} = \frac{\mbox{Distance}}{\mbox{Time}}= \frac{360~\mbox{km}}{4~\mbox{h}} = 90~\mbox{km/h}. \ _\square \]

When working with these problems, always pay attention to the units for speed, distance, and time. Converting units may be necessary to obtaining a correct answer.

A horse is trotting along at a constant speed of 8 miles per hour. How many miles will it travel in 45 minutes? The equation for calculating distance is \[\mbox{Distance} = \mbox{Speed} \times \mbox{Time},\] but we won't arrive at the correct answer if we just multiply 8 and 45 together, as the answer would be in units of \(\mbox{miles} \times \mbox{minute} / \mbox{hour}\). To fix this, we incorporate a unit conversion: \[\mbox{Distance} = \frac{8~\mbox{miles}}{~\mbox{hour}} \times 45~\mbox{minutes} \times \frac{1~\mbox{hour}}{60~\mbox{minutes}} = 6~\mbox{miles}. \ _\square \] Alternatively, we can convert the speed to units of miles per minute and calculate for distance: \[\mbox{Distance} = \frac{2}{15}~\frac{\mbox{miles}}{\mbox{minute}} \times 45~\mbox{minutes} = 6~\mbox{miles},\] or we can convert time to units of hours before calculating: \[\mbox{Distance} = 8~\frac{\mbox{miles}}{\mbox{hour}} \times \frac{3}{4}~\mbox{hours} = 6~\mbox{miles}.\] Any of these methods will give the correct units and answer. \(_\square\)

In more involved problems, it is convenient to use variables such as \(v\), \(d\), and \(t\) for speed, distance, and velocity, respectively.

Alice, Bob, Carly, and Dave are in a flying race!

Alice's plane is twice as fast as Bob's plane. When Alice finishes the race, the distance between her and Carly is \(D.\) When Bob finishes the race, the distance between him and Dave is \(D.\)

If Bob's plane is three times as fast as Carly's plane, then how many times faster is Alice's plane than Dave's plane?

Albert and Danny are running in a long-distance race. Albert runs at 6 miles per hour while Danny runs at 5 miles per hour. You may assume they run at a constant speed throughout the race. When Danny reaches the 25 mile mark, Albert is exactly 40 minutes away from finishing. What is the race's distance in miles? \[\] Let's begin by calculating how long it takes for Danny to run 25 miles: \[\mbox{Time} = \frac{\mbox{Distance}}{\mbox{Speed}}= \frac{25~\mbox{miles}}{5~\mbox{miles/hour}}= 5~\mbox{hours}.\] So, it will take Albert \(5~\mbox{hours} + 40~\mbox{minutes}\), or \(\frac{17}{3}~\mbox{hours}\), to finish the race. Now we can calculate the race's distance: \[\begin{align} \mbox{Distance} &= \mbox{Speed} \times \mbox{Time} \\ &= (6~\mbox{miles/hour}) \times \left(\frac{17}{3}~\mbox{hours}\right) \\ &= 34~\mbox{miles}.\ _\square \end{align}\]

A cheetah spots a gazelle \(300\text{ m}\) away and sprints towards it at \(100\text{ km/h}.\) At the same time, the gazelle runs away from the cheetah at \(80\text{ km/h}.\) How many seconds does it take for the cheetah to catch the gazelle? \[\] Let's set up equations representing the distance the cheetah travels and the distance the gazelle travels. If we set distance \(d\) equal to \(0\) as the cheetah's starting point, we have \[\begin{align} d_\text{cheetah} &= 100t \\ d_\text{gazelle} &= 0.3 + 80t. \end{align}\] Note that time \(t\) here is in units of hours, and \(300\text{ m}\) was converted to \(0.3\text{ km}.\) The cheetah catches the gazelle when \[\begin{align} d_\text{cheetah} &=d_\text{gazelle} \\ 100t &= 0.3 + 80t \\ 20t &= 0.3 \\ t &= 0.015~\mbox{hours}. \end{align}\] Converting that answer to seconds, we find that the cheetah catches the gazelle in \(54~\mbox{seconds}\). \(_\square\)

Two friends are crossing a hundred meter railroad bridge when they suddenly hear a train whistle. Desperate, each friend starts running, one towards the train and one away from the train. The one that ran towards the train gets to safety just before the train passes, and so does the one that ran in the same direction as the train.

If the train is five times faster than each friend, then what is the train-to-friends distance when the train whistled (in meters)?

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Time, Velocity, and Speed

Learning objectives.

By the end of this section, you will be able to:

• Explain the relationships between instantaneous velocity, average velocity, instantaneous speed, average speed, displacement, and time.
• Calculate velocity and speed given initial position, initial time, final position, and final time.
• Derive a graph of velocity vs. time given a graph of position vs. time.
• Interpret a graph of velocity vs. time.

Figure 1. The motion of these racing snails can be described by their speeds and their velocities. (credit: tobitasflickr, Flickr)

There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion.

As discussed in Physical Quantities and Units , the most fundamental physical quantities are defined by how they are measured. This is the case with time. Every measurement of time involves measuring a change in some physical quantity. It may be a number on a digital clock, a heartbeat, or the position of the Sun in the sky. In physics, the definition of time is simple— time is change , or the interval over which change occurs. It is impossible to know that time has passed unless something changes.

The amount of time or change is calibrated by comparison with a standard. The SI unit for time is the second, abbreviated s. We might, for example, observe that a certain pendulum makes one full swing every 0.75 s. We could then use the pendulum to measure time by counting its swings or, of course, by connecting the pendulum to a clock mechanism that registers time on a dial. This allows us to not only measure the amount of time, but also to determine a sequence of events.

How does time relate to motion? We are usually interested in elapsed time for a particular motion, such as how long it takes an airplane passenger to get from his seat to the back of the plane. To find elapsed time, we note the time at the beginning and end of the motion and subtract the two. For example, a lecture may start at 11:00 A.M. and end at 11:50 A.M., so that the elapsed time would be 50 min. Elapsed time Δ t is the difference between the ending time and beginning time,

where Δ t is the change in time or elapsed time, t f is the time at the end of the motion, and t 0 is the time at the beginning of the motion. (As usual, the delta symbol, Δ , means the change in the quantity that follows it.)

Life is simpler if the beginning time t 0 is taken to be zero, as when we use a stopwatch. If we were using a stopwatch, it would simply read zero at the start of the lecture and 50 min at the end. If t 0  = 0 , then Δ t  =  t f  ≡  t .

In this text, for simplicity’s sake,

• motion starts at time equal to zero ( t 0 = 0)
• the symbol t is used for elapsed time unless otherwise specified (Δ t  =  t f  ≡  t )

Your notion of velocity is probably the same as its scientific definition. You know that if you have a large displacement in a small amount of time you have a large velocity, and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour.

Average Velocity

Average velocity is displacement (change in position) divided by the time of travel ,

where[latex]\bar{v}[/latex] is the average (indicated by the bar over the v ) velocity, Δ x is the change in position (or displacement), and x f and x 0 are the final and beginning positions at times t f and t 0 , respectively. If the starting time t 0 is taken to be zero, then the average velocity is simply

Notice that this definition indicates that velocity is a vector because displacement is a vector . It has both magnitude and direction. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use. Suppose, for example, an airplane passenger took 5 seconds to move −4 m (the negative sign indicates that displacement is toward the back of the plane). His average velocity would be

[latex]\bar{v}=\frac{\Delta x}{t}=\frac{-4\text{m}}{5\text{s}}=-\text{0.8 m/s.}[/latex]

The minus sign indicates the average velocity is also toward the rear of the plane.

The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals.

Figure 2. A more detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip.

The smaller the time intervals considered in a motion, the more detailed the information. When we carry this process to its logical conclusion, we are left with an infinitesimally small interval. Over such an interval, the average velocity becomes the instantaneous velocity or the velocity at a specific instant . A car’s speedometer, for example, shows the magnitude (but not the direction) of the instantaneous velocity of the car. (Police give tickets based on instantaneous velocity, but when calculating how long it will take to get from one place to another on a road trip, you need to use average velocity.) Instantaneous velocity v is the average velocity at a specific instant in time (or over an infinitesimally small time interval).

Mathematically, finding instantaneous velocity, v , at a precise instant t can involve taking a limit, a calculus operation beyond the scope of this text. However, under many circumstances, we can find precise values for instantaneous velocity without calculus.

In everyday language, most people use the terms “speed” and “velocity” interchangeably. In physics, however, they do not have the same meaning and they are distinct concepts. One major difference is that speed has no direction. Thus speed is a scalar . Just as we need to distinguish between instantaneous velocity and average velocity, we also need to distinguish between instantaneous speed and average speed.

Instantaneous speed is the magnitude of instantaneous velocity. For example, suppose the airplane passenger at one instant had an instantaneous velocity of −3.0 m/s (the minus meaning toward the rear of the plane). At that same time his instantaneous speed was 3.0 m/s. Or suppose that at one time during a shopping trip your instantaneous velocity is 40 km/h due north. Your instantaneous speed at that instant would be 40 km/h—the same magnitude but without a direction. Average speed, however, is very different from average velocity. Average speed is the distance traveled divided by elapsed time.

We have noted that distance traveled can be greater than displacement. So average speed can be greater than average velocity, which is displacement divided by time. For example, if you drive to a store and return home in half an hour, and your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero, because your displacement for the round trip is zero. (Displacement is change in position and, thus, is zero for a round trip.) Thus average speed is not simply the magnitude of average velocity.

Figure 3. During a 30-minute round trip to the store, the total distance traveled is 6 km. The average speed is 12 km/h. The displacement for the round trip is zero, since there was no net change in position. Thus the average velocity is zero.

Another way of visualizing the motion of an object is to use a graph. A plot of position or of velocity as a function of time can be very useful. For example, for this trip to the store, the position, velocity, and speed-vs.-time graphs are displayed in Figure 4. (Note that these graphs depict a very simplified model of the trip. We are assuming that speed is constant during the trip, which is unrealistic given that we’ll probably stop at the store. But for simplicity’s sake, we will model it with no stops or changes in speed. We are also assuming that the route between the store and the house is a perfectly straight line.)

Figure 4. Position vs. time, velocity vs. time, and speed vs. time on a trip. Note that the velocity for the return trip is negative.

Making Connections: Take-Home Investigation—Getting a Sense of Speed

If you have spent much time driving, you probably have a good sense of speeds between about 10 and 70 miles per hour. But what are these in meters per second? What do we mean when we say that something is moving at 10 m/s? To get a better sense of what these values really mean, do some observations and calculations on your own:

• calculate typical car speeds in meters per second
• estimate jogging and walking speed by timing yourself; convert the measurements into both m/s and mi/h
• determine the speed of an ant, snail, or falling leaf

Check Your Understanding

A commuter train travels from Baltimore to Washington, DC, and back in 1 hour and 45 minutes. The distance between the two stations is approximately 40 miles. What is (a) the average velocity of the train, and (b) the average speed of the train in m/s?

(a) The average velocity of the train is zero because x f  =  x 0 ; the train ends up at the same place it starts.

(b) The average speed of the train is calculated below. Note that the train travels 40 miles one way and 40 miles back, for a total distance of 80 miles.

Section Summary

• Time is measured in terms of change, and its SI unit is the second (s). Elapsed time for an event is Δ t  =  t f  −  t 0 , where  t f  is the final time and  t 0  is the initial time. The initial time is often taken to be zero, as if measured with a stopwatch; the elapsed time is then just t .
• Average velocity [latex]\bar{v}[/latex] is defined as displacement divided by the travel time. In symbols, average velocity is [latex]\stackrel{-}{v}=\frac{\Delta x}{\Delta t}=\frac{{x}_{\text{f}}-{x}_{0}}{{t}_{\text{f}}-{t}_{0}}[/latex].
• The SI unit for velocity is m/s.
• Velocity is a vector and thus has a direction.
• Instantaneous velocity  v is the velocity at a specific instant or the average velocity for an infinitesimal interval.
• Instantaneous speed is the magnitude of the instantaneous velocity.
• Instantaneous speed is a scalar quantity, as it has no direction specified.
• Average speed is the total distance traveled divided by the elapsed time. (Average speed is not the magnitude of the average velocity.) Speed is a scalar quantity; it has no direction associated with it.

Conceptual Questions

1. Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.

2. There is a distinction between average speed and the magnitude of average velocity. Give an example that illustrates the difference between these two quantities.

3. Does a car’s odometer measure position or displacement? Does its speedometer measure speed or velocity?

4. If you divide the total distance traveled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity? Under what circumstances are these two quantities the same?

5. How are instantaneous velocity and instantaneous speed related to one another? How do they differ?

Problems & Exercises

1. (a) Calculate Earth’s average speed relative to the Sun. (b) What is its average velocity over a period of one year?

2. A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter’s frame of reference. (b) What is its average velocity over one revolution?

3. The North American and European continents are moving apart at a rate of about 3 cm/y. At this rate how long will it take them to drift 500 km farther apart than they are at present?

4. Land west of the San Andreas fault in southern California is moving at an average velocity of about 6 cm/y northwest relative to land east of the fault. Los Angeles is west of the fault and may thus someday be at the same latitude as San Francisco, which is east of the fault. How far in the future will this occur if the displacement to be made is 590 km northwest, assuming the motion remains constant?

5. On May 26, 1934, a streamlined, stainless steel diesel train called the Zephyr set the world’s nonstop long-distance speed record for trains. Its run from Denver to Chicago took 13 hours, 4 minutes, 58 seconds, and was witnessed by more than a million people along the route. The total distance traveled was 1633.8 km. What was its average speed in km/h and m/s?

6. Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon’s orbit increases by 3.84 × 10 6 m (1%)?

7. A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km. The trip took 18.0 min. (a) What was her average speed? (b) If the straight-line distance from her home to the university is 10.3 km in a direction 25.0° south of east, what was her average velocity? (c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity for the entire trip?

8. The speed of propagation of the action potential (an electrical signal) in a nerve cell depends (inversely) on the diameter of the axon (nerve fiber). If the nerve cell connecting the spinal cord to your feet is 1.1 m long, and the nerve impulse speed is 18 m/s, how long does it take for the nerve signal to travel this distance?

9. Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from the Earth to the Moon and back (that is, neglecting any time delays in the electronic equipment). Calculate the distance from Earth to the Moon given that the echo time was 2.56 s and that radio waves travel at the speed of light (3.00 × 10 8  m/s).

10. A football quarterback runs 15.0 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Calculate his average velocity (a) for each of the three intervals and (b) for the entire motion.

11. The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06 × 10 -10 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20 × 10 6  m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron’s average velocity?

Selected Solutions to Exercises & Problems

1. 3.0 × 10 4  m/s

3. 2 × 10 7 years

5. 34.689 m/s = 124.88 km/h

7. (a) 40 km/h (b) 43.4 km/h (c) average speed = 3.20 km/h [latex]\bar{v}=0[/latex].

9. 384,000 km

11. (a) 6.61 × 10 15 rev/s (b) 0 m/s

• College Physics. Authored by : OpenStax College. Located at : http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics . License : CC BY: Attribution . License Terms : Located at License

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Suppose that you were driving a car with the steering wheel turned in such a manner that your car followed the path of a perfect circle with a constant radius. And suppose that as you drove, your speedometer maintained a constant reading of 10 mi/hr. In such a situation as this, the motion of your car could be described as experiencing uniform circular motion. Uniform circular motion is the motion of an object in a circle with a constant or uniform speed.

Calculation of the Average Speed

Uniform circular motion - circular motion at a constant speed - is one of many forms of circular motion. An object moving in uniform circular motion would cover the same linear distance in each second of time. When moving in a circle, an object traverses a distance around the perimeter of the circle. So if your car were to move in a circle with a constant speed of 5 m/s, then the car would travel 5 meters along the perimeter of the circle in each second of time. The distance of one complete cycle around the perimeter of a circle is known as the circumference . With a uniform speed of 5 m/s, a car could make a complete cycle around a circle that had a circumference of 5 meters. At this uniform speed of 5 m/s, each cycle around the 5-m circumference circle would require 1 second. At 5 m/s, a circle with a circumference of 20 meters could be made in 4 seconds; and at this uniform speed, every cycle around the 20-m circumference of the circle would take the same time period of 4 seconds. This relationship between the circumference of a circle, the time to complete one cycle around the circle, and the speed of the object is merely an extension of the average speed equation stated in Unit 1 of The Physics Classroom .

The circumference of any circle can be computed using from the radius according to the equation

Combining these two equations above will lead to a new equation relating the speed of an object moving in uniform circular motion to the radius of the circle and the time to make one cycle around the circle ( period ).

The Direction of the Velocity Vector

To summarize, an object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. While the speed of the object is constant, its velocity is changing. Velocity, being a vector, has a constant magnitude but a changing direction. The direction is always directed tangent to the circle and as the object turns the circle, the tangent line is always pointing in a new direction.

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The ball will move along a path which is tangent to the spiral at the point where it exits the tube. At that point, the ball will no longer curve or spiral, but rather travel in a straight line in the tangential direction.

• Newton's Second Law - Revisited

All Subjects

Average travel speed

In transportation systems engineering.

Average travel speed is the overall speed at which vehicles move over a given distance, typically expressed in miles per hour (mph) or kilometers per hour (km/h). It is a critical measure in transportation systems, reflecting the efficiency of road networks and the impact of traffic conditions on travel times. Understanding average travel speed helps in assessing traffic flow, planning infrastructure improvements, and analyzing the performance of traffic management strategies.

congrats on reading the definition of average travel speed . now let's actually learn it.

5 Must Know Facts For Your Next Test

• Average travel speed can be influenced by various factors including road design, traffic signal timings, and vehicle interactions.
• In traffic management systems, measuring average travel speed helps identify congestion hotspots and evaluate the effectiveness of implemented measures.
• Higher average travel speeds are often associated with better level of service on roadways, leading to improved mobility for all users.
• Average travel speed calculations can vary based on the time of day, with peak hours typically showing lower speeds due to increased traffic volumes.
• Understanding average travel speed is essential for estimating vehicle emissions and fuel consumption, impacting environmental assessments.

Review Questions

• Average travel speed is a key indicator used to evaluate the effectiveness of Advanced Traffic Management Systems (ATMS). These systems aim to optimize traffic flow by using real-time data to manage signals, reduce congestion, and improve overall travel efficiency. By analyzing average travel speeds before and after implementing ATMS strategies, planners can assess how well these systems mitigate delays and enhance roadway performance.
• Changes in average travel speed directly affect Level of Service (LOS) calculations, which assess roadway performance based on factors like speed, density, and delay. A decrease in average travel speed typically indicates increased congestion, leading to poorer LOS ratings. Understanding this relationship helps engineers design roads that maintain higher speeds during peak periods, ultimately improving the overall quality of transportation facilities and user satisfaction.
• Fluctuating average travel speeds have significant implications for urban planning and policy development. When average speeds decrease due to congestion or inadequate infrastructure, planners may need to consider implementing new traffic management strategies or expanding existing road networks. Additionally, these fluctuations can inform policies aimed at promoting alternative modes of transportation such as public transit or cycling, ultimately contributing to more sustainable urban environments. Analyzing trends in average travel speeds enables policymakers to make informed decisions that enhance mobility and accessibility in urban areas.

Related terms

Traffic Flow : The movement of vehicles along a road or network, characterized by the number of vehicles passing a point in a given time period.

Congestion : A situation where the demand for road space exceeds the available capacity, leading to reduced average travel speeds and increased travel times.

Travel Time Reliability : The consistency of travel times for a particular route or segment, which is important for travelers' planning and decision-making.

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• Intelligent Transportation Systems

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• Physics Formulas

Average Speed Formula

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction. Let us know how to calculate average speed, the average speed formula, and solved examples on average speed.

Formula of Average Speed

The formula for average speed is found by calculating the ratio of the total distance traveled by the body to the time taken to cover that distance.

The average speed equation is articulated as:

Equation (2) is the formula for an average speed of an object moving at a varying speed.

Average Speed Solved Examples

Problem 1:  A runner sprints at a track meet. He completes a 1000-meter lap in 1 minute 30 sec. After the finish, he is at the starting point. Calculate the average speed of the runner during this lap? Answer:

Total distance covered by the runner = 1000 meters

Total time taken =1minute 30 sec

= 90 sec So, applying the formula for the average speed we have,

Problem 2 : A car travels at a speed of  40 km/hr for 2  hours and then decides to slow down to 30 km/hr for the next 2 hours. What is the average speed? Answer: D1 = 40 * 2 = 80 miles

D2 = 30 * 2 = 60 miles

Total distance D= D1+D2

D = 80 + 60

D = 140 miles

See the video below, to have a clear idea about average speed, average speed formula, and average velocity.

Hope you learned the average speed definition, average speed formula, how to calculate average speed along with examples. Stay tuned with BYJU’S to know more.

Frequently Asked Questions – FAQs

What is average speed.

The average speed is the total distance traveled by the object in a particular time interval.

Write the average speed formula?

Average speed = Total Distance traveled/Total Time taken

Is Average speed a scalar or vector quantity?

Define average velocity., what is the si unit of average velocity.

The SI unit of average velocity is meters per second.

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Average Speed Formula: Definition, Examples, Facts,  FAQs

What is the average speed formula, average speed formula, how to find average speed, solved examples on average speed formula, practice problems for average speed, frequently asked questions on average speed formula.

The average speed formula is given by the total distance traveled divided by the time taken to cover that distance.

The formula to find average speed is

Average speed $= \frac{Total \;distance}{Time}$

Observe the car in the given image. The distance it covers in the different time intervals is different. The speed of the car is not constant.

When you travel from one place to another by some vehicle, the speed changes from time to time. You do not travel with the same speed throughout the journey. The average speed, as the name itself suggests, gives us the mean value or the average value of the speed at which you traveled. 

It is kind of an estimate to understand the speed by which an object finishes its journey. It provides insights into how fast an object is moving over a given distance and time. Calculating average speed allows us to estimate travel times and make comparisons between different routes or means of transportation.

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The average speed formula can be given by 

Average Speed $=$ Total distance covered $\div$ Total time taken

Average speed formula for a round trip

Alt tag: Average speed formula for the round journey

Derivation:

Suppose you travel a distance “d” from A to B with the speed of x miles per hour and the distance from B to A with the speed of y miles per hour. In this case, the same distance is covered (both ways) but with the different speeds. In this case, the average speed is given by

Total distance traveled $= d + d = 2d$

Time taken to go from A to B $= \frac{Distance}{Speed} = dx$

Time taken to go from B to A $= \frac{Distance}{Speed} = dy$

Total time taken $= \frac{d}{x} + \frac{d}{y} = \frac{d(x + y)}{xy}$

Average speed $=$ Total distance covered $÷$ Total time taken

Thus, the average speed equation becomes

 Average speed $= \frac{2d}{\frac{d(x + y)}{xy}} = \frac{2xy}{x + y}$

Let’s understand steps to calculate average speed of an object . Let’s examine the procedure in more detail:

Step 1: Calculate the total distance traveled. If the two different speeds of the given journey are given, calculate the two distances separately using the formula: distance = Speed × time.

Step 2: Calculate the time taken to travel the total distance.

Step 3: Divide the total distance by total time taken to find the average speed. Assign the unit depending on the units of distance and time. For example, if the distance is given in miles and the time is in hours, the average speed will be measured in miles per hour (written as miles/hr).

Example 1: Joy travels the distance of 42 miles in 3 hours and 26 miles in 2 hours. Find his average speed.

Total distance traveled $= 42 + 26 = 68$ miles

Total time taken $= 3 + 2 = 5$ hours

Average speed $= \farc{68}{5} = 13.6$ miles/hr

Example 2: A bus travels the first 3 hours of journey with the speed of 20 miles/hour and the next 2 hours of the journey with the speed of 25 miles per hour. Find its average speed.

Distance $=$ Speed $\times$ time

The distance traveled in the first 3 hours with the speed of 20 mph $= 20 \times 3 = 60$ miles

The distance traveled in the next 2 hours with the speed of 25 mph $= 25 \times 2 = 50$ miles

Total distance traveled $= 60 + 50 = 110$ miles

Average speed $= \frac{110}{5} = 22$ miles/hour

Facts about Average Speed Formula

• Average speed is a scalar quantity, which can only be represented by magnitude. It has no direction.
• Average speed is independent of the direction of travel; it only depends on the total distance and time.
• It is essential to differentiate average speed from average velocity. Average velocity is a vector quantity that considers both magnitude and direction.

The average speed formula is calculated by dividing the total distance covered by the total time taken. In this article, we explored the concept of average speed, its formulas with different cases, and examples. Let’s solve a few examples and practice problems based on these concepts.

1. John walks a distance of 5 miles in 2 hours. Calculate his average speed.

Solution:  

Using the average speed formula , we get

Average speed $= \frac{Total \;Distance}{Total \;Time}$

Average speed $= \frac{5 \;miles}{2 \;hours}$

Average Speed $= 2.5$ miles/hour

2. A car travels at a speed of  24 miles/hr for 2 hours and then decides to slow down to 18 miles/hr for the next 2 hours. What is the average speed?

The distance traveled in the first 2 hours with the speed of 24 mph $= 24 \times 2 = 48$ miles

The distance traveled in the next 2 hours with the speed of 18 mph $= 18 \times 2 = 36$ miles

Total distance traveled $= 48 + 36 = 84$ miles

Total time taken$ = 2 + 2 = 4$ hours

Average speed $= \frac{84}{4} = 21$ miles/hour

3. Walter drives at a speed of 60 mph from his house to his office every day. He returns from work at the speed of 45 mph. What’s his average speed for the round trip?

Solution: 

Walter travels the same distance (both ways) with different speeds. We will use the average speed formula for the round trip.

$x = 60$ mph speed with which Walter travels from home to office

$y = 45$ mph speed with which Walter travels back to home from office

Average speed $= \frac{2xy}{x + y} = \frac{2\times 60 \times45}{60 + 45} = \frac{210}{105} = 51.42$ miles/hour

Average Speed Formula: Definition, Examples, Facts,  FAQs

Attend this quiz & Test your knowledge.

A kid walks a distance of 5 miles in 3 hours. What is the average speed?

A runner completes the first 1.5 hours of a race with the speed of 9 miles per hour and the next 1 hour with the speed of 10 miles per hour. what is the runner's average speed, if a car covers distances $d_{1},\; d_{2}$, and $d_{3}$ for time intervals $t_{1},\; t{_2}$, and $t_{3}$ respectively, the average speed is.

What is the average speed calculation formula?

Average Speed $=$ Total Distance / Total Time is the average speed equation .

What distinguishes average speed from average velocity?

While average velocity accounts for both magnitude and direction, average speed solely takes into consideration the amplitude of motion.

Can average speed be negative?

Average speed does not have direction and it can only be positive or zero.

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