As with many math problems, there are at least a couple of ways you can work this.
1. Figure average rate of change in the usual way:
[tex]\dfrac{f(5)-f(2)}{5-2}=\dfrac{400-(64)}{3}=\dfrac{336}{3}\\=112\quad\text{feet per second}[/tex]
2. Realize that the downward speed is increasing at a constant rate (32 ft/s²), so the average speed on the interval will be the speed at the midpoint of the interval: t = (2+5)/2 = 3.5 seconds. Since the downward speed started from zero, at t=3.5, it is
(3.5 s)×(32 ft/s²) = 112 ft/s
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The appropriate choice is ...
... C.The ball falls down with an average speed of 112 feet per second from 2 seconds to 5 seconds.
