MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A runner starts from rest at t=0. His distance from the start increases uniformly to 15m at t=3s. Thereafter his motion becomes non-uniform and his distance reaches 45m at t=9s. At t=6s the distance–time curve passes through point (6s,30m). A tangent drawn to the curve at this point passes through the additional point (5s,24m).
(a) Calculate the average speed of the runner for the whole 9s journey.
(b) Find his instantaneous speed at t=6s."