The velocity v(t) of a runner along a straight track is measured every 4 seconds during a 20-second sprint. The data are shown below.
t (s)
0
4
8
12
16
20
v(t) (m/s)
0.0
3.5
5.8
6.4
6.1
5.2
(a) Using the data in the table and assuming the velocity varies linearly between consecutive measurement times, approximate the total distance, in meters, the runner travels during the 20-second interval.
(b) Based on the pattern of the velocity values, determine whether your approximation in part (a) is likely to be greater than, less than, or equal to the exact value of ∫020v(t)dt. Justify your conclusion.