A runner’s velocity along a straight course is modeled by meters per second for
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A runner’s velocity along a straight course is modeled by v(t)=t+16−1 meters per second for 0≤t≤9, where t is measured in seconds.
(a) Verify that the runner’s velocity is continuous on [0,9] and differentiable on (0,9).
(b) Compute the runner’s average acceleration on [2,7]. Show all work leading to your answer, including units.
(c) Determine all times t in (2,7) at which the instantaneous acceleration equals the average acceleration found in part (b). Clearly justify each value obtained.
(d) Evaluate v(t) at each time found in part (c) and interpret the significance of these speed values in the context of the runner’s performance.