A bicycle’s speed v (in meters per second) is recorded at various times during a 6-second sprint. The data are shown in the table.
Time t (s): 0 1 3 4 6
Speed v (m/s): 0 5.8 7.1 6.5 5.2
(a) Using the right endpoint of each subinterval listed in the table, approximate the distance traveled during the sprint by writing and evaluating the corresponding Riemann sum.
(b) Interpret your numerical answer from part (a) in the context of the sprint, including appropriate units.
(c) Given that the speed of the bicycle decreases throughout the final two seconds, discuss whether the approximation in part (a) is an underestimate or an overestimate of the actual distance. Justify your answer.
(a) — see stem