A particle moves according to the law of motion $s(t) = t^{3}-6t^{2}+4t$, $t\ge 0$, where $t$ is measured in seconds and $s$ in feet.

a.) Find the velocity at time $t$.
Answer:

b.) What is the velocity after $3$ seconds?
Answer:

c.) When is the particle at rest? Enter your answer as a comma separated list. Enter None if the particle is never at rest.
At $t_1=$ and $t_2=$ with $t_1<t_2$.

d.) When is the particle moving in the positive direction?
When $0\leq t<$ and $t>$