Chapter 5.7, Problem 14ES

A particle moves with acceleration $a\left(t\right){\text{m/s}}^2$ along an $s\text{-axis}$ and has velocity ${\upsilon }_0\text{m/s}$ at time $t=0$ . Find the displacement and the distance traveled by the particle during the given time interval.

$a\left(t\right)=t-2;{\upsilon }_0=0;1\le t\le 5$