Chapter 13.3, Problem 38E

Velocity Work these exercises. (See Example 5.)

A student takes off running to class, but slows down when she realizes that she will make it on time. The velocity of the student after t seconds is

$v\left(t\right)=7t{e}^{-t/5}\left(0\le t\le 15\right).$

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

b. If it took 15 seconds to get to class, find and interpret $s\left(15\right)$ to the nearest integer.