Chapter 5.7, Problem 15ES

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.

$a\left(t\right)=1/\sqrt{3t+1};{\upsilon }_0=\frac{4}{3};1\le t\le 5$