The Derivative · Challenge problem

A particle moves along a line with position $s(t)=t^{3}-6t^{2}+9t$ (meters) for $t\ge 0$ (seconds). Find (a) the velocity and acceleration; (b) the times the particle is at rest; (c) when it moves right and when it moves left; (d) the total distance traveled on $[0,4]$; (e) the time intervals on which the particle's speed is increasing.