A particle moves according to a law of motion s = f(t), t ≥ 0, where is measured in seconds and 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 and after 3 s.
(h) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 8.