A particle moves along a horizontal line so that its velocity (in meters per second)…

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

Problem

A particle moves along a horizontal line so that its velocity (in meters per second) at time

t

seconds is given by

v(t)=3t^{2}-12t+5

for

0\le t\le 4

. (a) Calculate the displacement

\displaystyle \int_{0}^{4} v(t)\,dt

. (b) Determine the average velocity on

[0,4]

. (c) Find any time(s) when

v(t)=0

[0,4]

and use them to discuss reversal of direction. (d) Interpret the sign of the average velocity.