law of motion

law of motion

1–4 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 3 s?
(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 8 s.
(f ) Draw a diagram like Figure 2 to illustrate the motion of the particle.
(g) Find the acceleration at time t and after 3 s.
(h) Graph the position, velocity, and acceleration functions for 0 = t = 8.
(i) When is the particle speeding up? When is it slowing down?
1. f (t) = t3 – 12t2 + 36t
2. f (t) = 0.01t4 – 0.04t3
3. f (t) = cos(pt/4), t = 10

4. f (t) = te–t/2