Period 1: AROC and Secants

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 distance
change in time

Δ d
Δ t

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 :)
-Ana