The acceleration function $($in $\frac{m}{s^2})$ and the initial velocity are given for a particle moving along a line.

$a(t)=t+8,v(0)=3,0t10$

$($a$)$ Find the velocity at time $t.$

$v(t)=$

$\frac{m}{s}$

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

$$ m