Question Video: Calculating the Average Speed and Velocity of a Body from a Graph Mathematics

Consider the graph. Complete the following: The average speed is _ m/s. Complete the following: According to the graph, the average velocity is _ m/s.

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Video Transcript

Consider the following graph. Complete the following: The average speed is what meters per second. Complete the following: According to the graph, the average velocity is what meters per second.

In this question, we are asked to calculate the average speed and average velocity shown in the graph. The horizontal axis shows the time measured in seconds, and the vertical axis shows the displacement measured in meters. We are asked to give both answers in meters per second.

The body begins at the origin and moves a distance of 20 meters away from this point in 10 seconds. It then changes direction and heads back to the origin, reaching this point after a further 10 seconds. We know that the average speed of an object is equal to the total distance traveled divided by the total time. From the graph, we saw that the object traveled a total of 40 meters, and it did this in a time of 20 seconds. As 40 divided by 20 is equal to two, the average speed is equal to two meters per second.

The average velocity, on the other hand, is equal to the net displacement divided by the total time. As already mentioned, the object starts and finishes at the same point. This means that the net displacement is zero meters. Dividing this by a total time of 20 seconds gives us zero meters per second. The average velocity is equal to zero meters per second.

We can go one stage further and conclude that whenever the net displacement is equal to zero, the average velocity will be equal to zero. This can be seen directly from the graph as the 𝑦-coordinates of the start and end point are both zero. The two missing numbers in the statements are two and zero.

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