I don't understand exactly what the question is asking for in (a) and for (e), I feel like I know what it's asking but I'm getting 32 feet which is exactly a third of the correct answer if that helps.:

Question

43.

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 3s?

(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 8s.

(f) Draw a diagram like Figure 7 to illustrate the motion of the particle.

Answer:

(a)3t^2 - 24t + 36

(e) 96 feet

My work is attached (#43).

Any help would be greatly appreciated!

Thanks in advance!