The acceleration function $($in $\frac{m}{s^2})$ and the initial velocity $v(0)($in $\frac{m}{s})$ are

$a(t)=2t2,v(0)=-15,0t5$

$($a$)$ Find the velocity $($in $\frac{m}{s})$ at time $t.$

$v(t)=\frac{m}{s}$

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

$$ m