Answer
Using the Midpoint Rule, we can estimate that the runner covered a distance of 45.23 meters during those 5 seconds.
Work Step by Step
We can choose five subintervals of the interval $[0,5]$
$\Delta t = \frac{b-a}{n} = \frac{5-0}{5} = 1$
We can find the midpoint of each subinterval:
$t_1 = 0.5$
$t_2 = 1.5$
$t_3 =2.5$
$t_4 = 3.5$
$t_5 = 4.5$
We can find an estimate for the distance $D$:
$D = \int_{0}^{5}~v(t)~dt \approx \sum_{i=1}^{5} v(t_i)~\Delta t$
$= (4.67+8.86+10.22+10.67+10.81)~(1)$
$= 45.23$
Using the Midpoint Rule, we can estimate that the runner covered a distance of 45.23 meters during those 5 seconds.
