A particle moves according to a law of motion s = f (t), t ≥ 0, where t is measured in seconds and s in feet.
(a) Find the velocity at time t.
(b) What is the velocity after 1 second?
(c) When is the particle at rest?
(d) When is the particle moving in the positive direction?
(e) Find the total distance traveled during the first 6 seconds.
(f) Draw a diagram like Figure 2 to illustrate the motion of the particle.
(g) Find the acceleration at time t and after 1 second.
(h) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6.
(i) When is the particle speeding up? When is it slowing down?

f (t) = t³ – 9t² + 24t