The motion of a particle along a straight line is described by equation: x = 8 + 12t - t³ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

CONCEPT: 

ACCELERATION & DECELEARATION:

• Acceleration is the measure of the rate of change of velocity with respect to time, the value of acceleration can be both positive and negative.  

​                                                                                                                                                                                                                   Where v= Final velocity, u =Initial velocity and t = time 

•  Deceleration is the negative rate of change of velocity.        

CALCULATION:

Given - x = 8 + 12t - t3

• As we know, velocity is defined as the rate of change of displacement.

When V = 0, then

⇒ 12 - 3t² = 0

⇒ 12 = 3t²

⇒ t = 2 sec

• The retardation is given by