#### Problem 73E

73. A particle moves on a vertical line so that its coordinate at time $t$ is $y=t^{3}-12 t+3, t \geqslant 0$.

(a) Find the velocity and acceleration functions.

(b) When is the particle moving upward and when is it moving downward?

(c) Find the distance that the particle travels in the time interval $0 \leqslant t \leqslant 3$.

(d) Graph the position, velocity, and acceleration functions for $0 \leqslant t \leqslant 3$.

(e) When is the particle speeding up? When is it slowing down?