Question

a particle moves along the x-axis so that its velocity at any time t is given by v(t)=3t^2-18t+24 and its position is given by x(t)=t^3-9t^2+24t+4.

A. For what values of t is the particle at rest?
B. Find the total distance traveled by the particle from T=1 to T=3.
Hint: the particle is moving to the left when v(t)<0 and to the right when v(t)>0.