Question

A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t³ − 9t² + 24t.

1. (a) Find the velocity at time t.
2. (b) What is the velocity after 1 second?
3. (c) When is the particle at rest?
4. (d) When is the particle moving in the positive direction?
5. (e) Find the total distance traveled during the first 6 seconds.
6. (f) Draw a diagram like Figure 2 to illustrate the motion of the particle.
7. (g) Find the acceleration at time t and after 1 second.
8.