A particle is moving in a straight line. The variation of position x as a function of time t is given as x = t 3 - 6 t 2 + 20 t + 15 m . The velocity of the body when its acceleration becomes zero is:

Step-by-step solution

Given the instantaneous position is x = t 3 - 6 t 2 + 20 t + 15 . . . 1 The velocity of the particle is given by v = d x d t = 3 t 2 - 12 t + 20 . . . 2 And, the acceleration of the particle is given by a = d v d t = 6 t - 12 . . . 3 When a = 0 , it implies 6 t - 12 = 0 ⇒ t = 2 s At t = 2 s , the velocity can be calculated as follows: v = 3 ( 2 ) 2 - 12 ( 2 ) + 20 = 8 m s - 1