Now, let us begin.
A line passing through at least two different points on a curve is called a secant. The average rate of change, abbreviated as AROC, is found by determining the slope of a secant on the graph. Therefore, Average rate of change=Slope of Secant.
In the investigation, Usain Bolt's 100m sprint in the 2008 Olympics was graphed. To determine the slope of a graph, we would normally use y2-y1/x2-x1. However, because we are looking at the average change in speed, it will be d2-d1/t1-t2. (final distance minus the original distance, divided by the final time minus the original time)
change in time
By calculating the AROC per 10m interval, we are able to find the rates of change for each segment of his race (m/s) - 5.4, 9.8, 10.99, 11.49, 11.76, 12.2, 12.2, 12.2...
We notice that his rate of change is increasing (he is getting faster). This makes sense because, the slope of the graph gets steeper and steeper.
Have a great week :)