A cyclist’s velocity v(t) (in meters per second) is recorded once each minute for eight minutes. The data are shown below.
Time t (min): 0 1 2 3 4 5 6 7 8
Velocity v(t) (m/s): 0 3 6 5 1 −2 −4 −1 0
(a) Estimate the cyclist’s displacement for 0≤t≤8 minutes using the eight one-minute subintervals shown in the table. Indicate the numerical method you select and show your calculation clearly.
(b) Using the same data, estimate the total distance traveled during the eight-minute ride.
(c) Use your answer from part (a) to estimate the cyclist’s average velocity (in meters per second) over the eight-minute interval, and interpret this value in context.