MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A sled moves along a straight, frictionless track so that its position (in meters) at time t≥0 seconds is given by s(t)=5t2/3.
(a) Write an expression for the average velocity of the sled over the time interval [0,h], where h>0.
(b) Use your expression from part (a) to determine whether the sled has a finite instantaneous velocity at t=0. Support your answer with appropriate limit reasoning.
(c) Interpret your result from part (b) in the context of the sled’s motion. What does it say about how the sled starts moving?
(d) Find all values of t>0 for which the sled’s velocity is zero. Provide justification.