Question: Problem 5: A particle moves according to a law of motion \(s\left( t \right)={{t}^{3}}-12{{t}^{2}}+36t,\,\,t\ge 0\), where t is measured in seconds and s is measured in meters.

a. Find the acceleration function for the particle.

b. What is the acceleration after 3 seconds?

c. Graph the position, velocity, and acceleration functions for 0 < t < 8

d. When is the particle speeding up?

e. When is it slowing down?