A particle moves along a straight line with velocity

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

Problem

v

, measured in meters per second, given by

v(t)=\begin{cases} 4, & 0\le t<2,\\ 8, & t=2,\\ 6-t, & 2< t\le 5, \end{cases}

where

t

is measured in seconds. (1) Compute the particle’s net displacement on the time interval

0\le t\le 5

by evaluating

\displaystyle\int_{0}^{5} v(t)\,dt

. Show how you account for the point

t=2

. (2) Determine the particle’s average velocity on

[0,5]

. Include a brief explanation of why the average velocity can be found even though

v

is not continuous at

t=2

. Express your answer in meters per second.