$(10$ Points Each$)$ A particle is moving along a straight$-$line path such that its velocity, in meters per second, at time $t($in seconds$)$ is given by the function $v(t)=4t^3-3t^2-60t+75,0t3.$

a$.$ When is the particle moving fastest over the interval $0,3?$

b$.$ How far does the particle travel over the interval $0,3?$