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Average Speed - Physics Video by Brightstorm

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Time-saving physics video explaining how to calculate average speed. Average speed is a scalar number calculated by dividing distance traveled by time elapsed.

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Describing motion: Speed, Velocity and Acceleration

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I saw this interesting tweet from @thephysicsgirl

Today, I taught Alan Alda the difference between speed and velocity. Life is complete.

- Physics Girl (@thephysicsgirl) June 2, 2014

But what is the difference? If you ask any person on the street, they might say there is no difference. In non-physics use, they would be correct. However, in physics we have very specific definitions for these terms. Surprisingly, not all textbooks agree on the definition of speed.

Let's start with the easy term: velocity. I'm pretty sure all the textbooks agree on this definition.

Velocity and Average Velocity ----------

I guess I should start from the beginning. There are two other important terms: position and displacement. Suppose that I have a moving object. It moves from location 1 to location 2 along the path shown below.

The position of location 1 is the vector from the origin to that point. Same for location 2 and the position vector 2. Position is a vector from the origin of your coordinate system to some particular point. If you change the location of the origin, your position vectors will change.

The displacement is the vector from location 1 to 2. This vector does NOT depend on the location of the origin. If you know the two position vectors, then the displacement vector would be:

Finally, we are ready for the definition of average velocity. When the object goes from position 1 to 2, it will take some time. I will call this time Δt. The average velocity would then be:

That's the average velocity. But what about just velocity? Technically, this would be called instantaneous velocity. This is just the limit as the time interval approaches zero. Of course that makes this a derivative with respect to time:

That's velocity. Pretty much everyone agrees on this definition.

Speed and Average Speed --------

There are two common definitions of speed that are used in textbooks. I looked through a sample of books in my office and all of them fell into one of two definitions.

Speed Definition 1: The average speed is the distance traveled divided by the time it took to travel this distance. If I use the symbol s for speed (which isn't a very good choice), then I would write:

You can see the problem here. How do you calculate distance? In the picture example above, this would be the length of that dotted line path. The average velocity only depends on the starting and ending point, not the path but the speed depends on the path (in this definition). Also with this definition, the average speed is a scalar quantity and not a vector quantity.

Oh, most of the textbooks used this definition of average speed.

Speed Definition 2: Speed is the magnitude of the velocity. That's it. As an equation, that would be:

This would also make speed a scalar value.

An Example ----

Here is a classic example showing the difference between average velocity and the two definitions of speed. Suppose you have a circular race track that has a circumference of 1000 meters. A car drives around the track such that it takes 50 seconds for a lap. What is the average velocity and the average speed?

For the average velocity, I need the vector position of the start and end of the motion. But wait! These are in the same spot! That means that the displacement is the zero vector (which is different than just zero). The average velocity is zero vector m/s. How can this be? Remember, that velocity is a vector. With an average velocity of zero (vector), that means the car is going just as much North as it is South so that these all average to zero (vector).

What about the average speed according to definition 1? In this case, the distance traveled is 1000 meter so that the average speed would be (1000 m)/(50 s) = 20 m/s. This is what the speedometer would read.

According to definition number 2, the average speed is the magnitude of the average velocity. Since the average velocity is zero (vector) m/s, the magnitude of this is also zero meters per second. If you want the instantaneous speed according to the definition 2, that would also be 20 m/s.

It's all about definitions ---------

Suppose we want to have a discussion about gardening. In this discussion, I keep talking about a hand shovel (a small shovel that you can use with one hand). However, you always call this a giant spoon so that when I say "hand shovel", you have no idea what I am talking about. This situation seems silly, but we have this exact problem in physics.

Consider the word momentum. Whenever I am having a discussion with students about physics and motion, this word tends to come up. But it is typically used to mean lots of different things - like pushing, energy, speed, and even momentum. In physics, we have a very explicit definition for momentum.

The momentum (at velocities not near the speed of light) is defined as the product of the mass and velocity of an object. This definition physicists (and textbooks) agree on. The definition of speed isn't always agreed on.
Homepage Image: Angelo DeSantis/Flickr

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What's the Difference Between Speed and Velocity?

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I saw this interesting tweet from @thephysicsgirl Today, I taught Alan Alda the difference between speed and velocity. Life is complete. - Physics Girl (@thephysicsgirl) June 2, 2014 But what is the difference? If you ask any person on the street, they might say there is no difference.

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Kids learn about speed and velocity in the science of physics and the laws of motion including units and measurement. What is the difference between speed and velocity?

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Speed & Velocity - The Physics Hypertextbook

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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.

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Just as distance and displacement have distinctly different meanings (despite their similarities), so do speed and velocity. Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time. Contrast this to a slow-moving object that has a low speed; it covers a relatively small amount of distance in the same amount of time. An object with no movement at all has a zero speed.

Velocity as a Vector Quantity

Velocity is a vector quantity that refers to "the rate at which an object changes its position." Imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity. Because the person always returns to the original position, the motion would never result in a change in position. Since velocity is defined as the rate at which the position changes, this motion results in zero velocity. If a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. Every step must go into moving that person further from where he or she started. For certain, the person should never change directions and begin to return to the starting position.

Velocity is a vector quantity. As such, velocity is direction aware. When evaluating the velocity of an object, one must keep track of direction. It would not be enough to say that an object has a velocity of 55 mi/hr. One must include direction information in order to fully describe the velocity of the object. For instance, you must describe an object's velocity as being 55 mi/hr, east. This is one of the essential differences between speed and velocity. Speed is a scalar quantity and does not keep track of direction; velocity is a vector quantity and is direction aware.

Determining the Direction of the Velocity Vector

The task of describing the direction of the velocity vector is easy. The direction of the velocity vector is simply the same as the direction that an object is moving. It would not matter whether the object is speeding up or slowing down. If an object is moving rightwards, then its velocity is described as being rightwards. If an object is moving downwards, then its velocity is described as being downwards. So an airplane moving towards the west with a speed of 300 mi/hr has a velocity of 300 mi/hr, west. Note that speed has no direction (it is a scalar) and the velocity at any instant is simply the speed value with a direction.

Calculating Average Speed and Average Velocity
As an object moves, it often undergoes changes in speed. For example, during an average trip to school, there are many changes in speed. Rather than the speed-o-meter maintaining a steady reading, the needle constantly moves up and down to reflect the stopping and starting and the accelerating and decelerating. One instant, the car may be moving at 50 mi/hr and another instant, it might be stopped (i.e., 0 mi/hr). Yet during the trip to school the person might average 32 mi/hr. The average speed during an entire motion can be thought of as the average of all speedometer readings. If the speedometer readings could be collected at 1-second intervals (or 0.1-second intervals or ... ) and then averaged together, the average speed could be determined. Now that would be a lot of work. And fortunately, there is a shortcut. Read on.

The average speed during the course of a motion is often computed using the following formula:

In contrast, the average velocity is often computed using this formula

Let's begin implementing our understanding of these formulas with the following problem:
Q: While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?
To compute her average speed, we simply divide the distance of travel by the time of travel.

That was easy! Lisa Carr averaged a speed of 55 miles per hour. She may not have been traveling at a constant speed of 55 mi/hr. She undoubtedly, was stopped at some instant in time (perhaps for a bathroom break or for lunch) and she probably was going 65 mi/hr at other instants in time. Yet, she averaged a speed of 55 miles per hour. The above formula represents a shortcut method of determining the average speed of an object.

Average Speed versus Instantaneous Speed

Since a moving object often changes its speed during its motion, it is common to distinguish between the average speed and the instantaneous speed. The distinction is as follows.

Instantaneous Speed - the speed at any given instant in time.

Average Speed - the average of all instantaneous speeds; found simply by a distance/time ratio.

You might think of the instantaneous speed as the speed that the speedometer reads at any given instant in time and the average speed as the average of all the speedometer readings during the course of the trip. Since the task of averaging speedometer readings would be quite complicated (and maybe even dangerous), the average speed is more commonly calculated as the distance/time ratio.

Moving objects don't always travel with erratic and changing speeds. Occasionally, an object will move at a steady rate with a constant speed. That is, the object will cover the same distance every regular interval of time. For instance, a cross-country runner might be running with a constant speed of 6 m/s in a straight line for several minutes. If her speed is constant, then the distance traveled every second is the same. The runner would cover a distance of 6 meters every second. If we could measure her position (distance from an arbitrary starting point) each second, then we would note that the position would be changing by 6 meters each second. This would be in stark contrast to an object that is changing its speed. An object with a changing speed would be moving a different distance each second. The data tables below depict objects with constant and changing speed.

Now let's consider the motion of that physics teacher again. The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity.

The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s.

Here is another example similar to what was seen before in the discussion of distance and displacement. The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Use the diagram to determine the average speed and the average velocity of the skier during these three minutes. When finished, click the button to view the answer.

As a last example, consider a football coach pacing back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D.

What is the coach's average speed and average velocity? When finished, click the button to view the answer.

In conclusion, speed and velocity are kinematic quantities that have distinctly different definitions. Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance (a scalar quantity) per time ratio. Speed is ignorant of direction. On the other hand, velocity is a vector quantity; it is direction-aware. Velocity is the rate at which the position changes. The average velocity is the displacement or position change (a vector quantity) per time ratio.

Visit Name That Motion.

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what is the difference between speed and a velocity

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Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance (a scalar quantity) per time ratio. Speed is ignorant of direction. On the other hand, velocity is a vector quantity; it is a direction-aware quantity.