The acceleration function $($in m$/$s$2)$ and the initial velocity v$(0)($in m$/$s$)$ are given for a particle moving along a line.

a$($t$)=2$t $+4,$ v$(0)=5,0$ t $3$

$($a$)$

Find the velocity $($in m$/$s$)$ at time t$.$

v$($t$)=$

t$2+4$t$5$

m$/$s

$($b$)$

Find the distance traveled $($in m$)$ during the given time interval.