A particle moves according to a law of motion s = f(t) = t3 – 12t2 + 36t, t > 0 , where is measured in seconds and in meters.
(a) Find the acceleration at time and after 3 s.
(b) Graph the position, velocity, and acceleration functions for 0 < y < 8.
(c) When is the particle speeding up? When is it slowing down?