Given a particle moving according to $s(t)=t^3-9t^2+15t+3$:
(A) Find the velocity function.
(B) What is the velocity after 3 seconds?
(C) When is the particle at rest? (List the smaller answer first.)
(D) Find the total distance traveled during the first 8 seconds. (Hint: When is the particle traveling in the positive direction?)

(A) $v(t)=$ ft/s
(B) $v(3)=$ ft/s
(C) $t=$ s     and $t=$ s
(D) $\text{distance}=$ ft