A particle moves along a straight line

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

Problem

A particle moves along a straight line. Its velocity, in meters per second, is given by

v(t)=6-3t

for

0\le t\le4

, where

t

is measured in seconds. (a) Determine the particle’s displacement, in meters, from

t=0

t=4

. (b) Determine the total distance, in meters, that the particle travels on the interval

0\le t\le4

. Show all work that supports your answer. (c) Explain, using the behavior of

v

, why the values found in parts (a) and (b) are different.