A particle moves along a straight track so that

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A particle moves along a straight track so that, for

0\le t\le 2

seconds, its velocity (in feet per second) is given by

v(t)=k\,(4-t^{2}),

where

k

is a non-zero constant. (a) Calculate the particle’s displacement over the interval

0\le t\le 2

in terms of

k

. Express your answer as a simplified exact value. (b) Determine the value of

k

for which the displacement over this interval is exactly

12

feet. (c) Using the value of

k

found in part (b), compute the particle’s average velocity on

0\le t\le 2

. Interpret the sign of your result in the context of the motion.