A runner completes a straight-line training run in which her position
MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives
Problem
A runner completes a straight-line training run in which her position, measured in meters from the starting line, is recorded at the beginning and end of the interval 0≤t≤12 minutes. At t=0 the position is 0 meters, and at t=12 minutes the position is 1800 meters. Assume the position function is continuous on [0,12] and differentiable on (0,12).
(a) Determine the runner’s average speed over the 12-minute interval. Express your answer in meters per second.
(b) Prove that there exists a time c with 0<c<12 minutes at which the runner’s instantaneous speed equals the average speed found in part (a).
(c) If the runner’s training plan requires her to reach an instantaneous speed of exactly 5 m/s at some point during the run, does the information provided guarantee that she met this requirement? Explain fully.