The position coordinate of a particle which is confined to move along a straight line is given by s= 2t³ - 24t + 6, where s is measured in meters from a convenient origin and t is in seconds. Determine (a) the time required for the particle to reach a velocity of 72 m/s from its initial condition at t = 0, (b) the acceleration of the particle when v= 30 m/s, and (c) the net displacement of the particle during the interval from t = 1 s to t = 4 s.

The position coordinate of a particle which is confined to move along a straight line is given by s= 2t³ - 24t + 6, where s is measured in meters from a convenient origin and t is in seconds. Determine (a) the time required for the particle to reach a velocity of 72 m/s from its initial condition at t = 0, (b) the acceleration of the particle when v= 30 m/s, and (c) the net displacement of the particle during the interval from t = 1 s to t = 4 s.