Physics Lesson 3.5.2 - The meaning of Average and Instantaneous Speed

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Welcome to our Physics lesson on The meaning of Average and Instantaneous Speed, this is the second lesson of our suite of physics lessons covering the topic of Speed and Velocity in 1 Dimension, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

The meaning of Average and Instantaneous Speed

In the previous example, we found the speed of winner athlete was 5 m/s. It is obvious this represents an average value, as it is impossible for the athlete to keep moving at this speed during the entire race. Normally an athlete runs faster at the beginning of a race and then he slows down, as he gets tired. Therefore, we use the concept of "average speed" to represent a motion, which is presumably irregular.

By definition, "The average speed < v > of an object refers to the total distance it travels divided by the time elapsed."

Mathematically, we write

< v > = stotal/ttotal

The utility of the average speed use is better observed in the following example.

Example 1

Physics Tutorials: This image shows

What is the average speed of the car (in km/h) during the entire trip?

Solution 1

It is obvious the motion has not been uniform during the trip. Therefore, we must use the concept of average speed to understand whether the car has moved fast or slowly during the process.

From the equation of the average speed

< v > = stotal/ttotal

and relying on the data shown in the figure, we see that

< v > = sAB + sBC + sCD + sDE/tAB + tBC + tCD + tDE

Substituting the values, we obtain for the average speed of the car

< v > = 70km + 100km + 60km + 90km/1h + 2h + 0.5h + 1.5h
= 320km/5h
= 64 km/h

On the other hand, Instantaneous Speed (v) is another important concept used in Kinematics. It shows the actual speed at which an object is moving. An example of application in daily life of the instantaneous speed concept is the car's speedometer. It shows the instantaneous speed of the car as it takes "live" measurements of the car's moving speed.

But how can we measure the instantaneous speed when an object is not doing a uniform motion and furthermore when its motion is quite irregular?

The procedure is not very simple. However, with the help of digital electronics this is a solved issue already. Basically, a very sensitive timer is used to partialize the motion in small intervals and for each interval the distance is calculated through a distance sensor. The speed cannot change drastically due to the object's "inertia" (look at the tutorial Newton's First Law of Motion. The Meaning of Inertia). Therefore, the average speed measured for each of the abovementioned small intervals of time represents the instantaneous speed of the object in that specific instant. The result obtained is accurate enough as any change in values is smooth considering the shortness of time intervals.

To calculate instantaneous speed, we need to divide the distance by time. However, we don't want to use the distance of the entire trip, because that will give us average speed. We take a small portion of distance and divide it by the corresponding (small) time interval. The smaller the distance (and the time interval) used, the more accurately we can measure the speed for that specific time.

The equation of instantaneous speed v is:

v = ∆s/∆t

where Δs represents the small distance considered and Δt the time interval during which the event occurs.

If it is possible to represent the motion in a graph this would be a huge advantage as the value of the instantaneous speed is calculated directly from the data shown in the graph. Look at the example below.

Example 2

The following graph shows the dependence of the Distance travelled by an object from the Time elapsed. Find the speed of the object at t = 4.4 s.

Physics Tutorials: This image shows

Solution 2

As explained before, we must take two neighbouring values for the distance (s1 and s2) and the time (t1 and t2), which must be as close as possible and then using the equation

v = ∆s/∆t= s2 - s1/t2 - t1

to calculate the instantaneous speed at the required instant.

Let's take for example t1 = 4.1 s and t2 = 4.6 s. The corresponding distances for these two time values are s1 = 15.0 m and s2 = 18.0 m respectively. Look at the figure:

Physics Tutorials: This image shows

Therefore, we obtain for the instantaneous speed at t = 4.4 s or as it is otherwise written, v (4.4):

v = ∆s/∆t
= s2-s1/t2-t1
= 18.0m - 15.0m/4.6s - 4.1s
= 3.0m/0.5s
=6 m/s

This is an approximate value, which becomes closer to the true value when the intervals become finer. However, it gives us a good idea on how the object is moving.

You have reach the end of Physics lesson 3.5.2 The meaning of Average and Instantaneous Speed. There are 4 lessons in this physics tutorial covering Speed and Velocity in 1 Dimension, you can access all the lessons from this tutorial below.

More Speed and Velocity in 1 Dimension Lessons and Learning Resources

Kinematics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
3.5Speed and Velocity in 1 Dimension
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
3.5.1What is Speed? How do we measure it?
3.5.2The meaning of Average and Instantaneous Speed
3.5.3What is Velocity? How do we measure it?
3.5.4Average and Instantaneous Velocity

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