A particle moves along the x-axis so that its position at any time t≥0 is given by x(t)=(t-2)^3 (t-6). a) Find the velocity and acceleration of the particle at any time t≥0.

b) Find the value of t when the acceleration is zero.

c) When is the particle moving to the right?

d) When is the velocity of the particle decreasing?

e) When is the speed of the particle increasing?