The acceleration function (in $m/s^2$) and initial velocity for a particle moving along a line is given by $$a(t)= 3 t + 12,\,\, v(0)=15,\,\, 0 \le t \le 10.$$

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

Velocity = meters

(b) Find the total distance traveled (in meters) by the particle.

Total distance traveled = meters