A robot has been programmed so that when it starts to move, its velocity after $t$

seconds will be $3t^2$ feet$/$second$.$

$($a$)$ How far will the robot travel during its first $4$ seconds of movement?

$($b$)$ How far will the robot travel during its next $4$ seconds of movement?

$($c$)$ How many seconds before the robot is $729$ feet from its starting place?