A car travels along a straight highway. The table below lists the odometer readings (total distance traveled, in miles) at selected times during the trip, as well as the speedometer reading (instantaneous speed, in miles per hour) at those same times.
Time t (hours): 0 1 2 3.5 5
Odometer reading D(t) (miles): 0 55 117 210 328
Speedometer reading v(t) (mph): 60 58 59 62 64
(a) Calculate the average speed of the car over the entire 5-hour trip. Show all work and include correct units.
(b) Determine whether there must exist a time c in the interval 0<t<5 at which the instantaneous speed v(c) equals the average speed found in part (a). Justify your answer using appropriate reasoning.
(c) The driver claims, “At exactly t=2 hours my instantaneous speed was 59 mph, so my average speed for the first two hours must also have been 59 mph.” Explain whether the driver’s claim must be true, providing clear justification.