Chapter 13.3, Problem 37E

Velocity Work these exercises. (See Example 5.)

A car was driving on a two-lane highway at 80 feet per second (about 55 mph) when it abruptly speeds up to pass a slow-moving truck. The velocity of the car (in ft/sec) after t seconds (see accompanying figure) is given by

$v\left(t\right)=80+10t{e}^{-t/4}\left(0\le t\le 30\right).$

a. Find and interpret $v\left(0\right),v\left(4\right)$, and $v\left(30\right)$.

b. Find a formula for the position function $s\left(t\right)$.