Distance time graph

Equations and graphs Distance time graph

The world record for the men’s 100 metres was set in 2009. The record is 9.58 seconds.

We can see that world record run on the distance time graph below

We can draw a straight line from the start of the race (0 seconds and 0 metres) to the end of the race (9.58 seconds and 100m metres) and by calculating the gradient of the line, work out the average speed over 100 metres when the world record was set.

The gradient is $\frac{100}{9.56} = 10.46ms^{-1}$

The gradient of the single straight line gives us the average speed over the full 100 metres. As the sprinters start from stationary the average speed for the race is quicker than the speed of the sprinter at the beginning of the race and slower in the middle and end when he has accelerated to his top speed.

The sprinter gets to his top speed after 20 metres. If we break the race up into three sections, the first 10 metres, the second 10 metres and the rest of the race then we will be a more accurate estimation of his speed during these sections of the race.

The gradient in these three sections are

The gradient in the first ten metres is $\frac{10}{1.88} = 5.32ms^{-1}$

The gradient in the second ten metres is $\frac{10}{1.00} = 10.00ms^{-1}$

The gradient in the last eighty metres is $\frac{80}{6.88} = 11.63ms^{-1}$

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