The motion of a particle along a straight line is described by equation $ x = 8 + 12t - t^3 $ where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero is
- $24\, m\, s^{-2}$
- zero
- $6\, m\, s^{-2}$
- $12\, m\, s^{-2}$
The Correct Option is D
Solution and Explanation
$v=\frac{d x}{d t}=12-3 t^{2}$
$a=\frac{d v}{d t}=-6 t$
putting $v =0$
$3 t ^{2}=12$
$t =2 sec$
$\therefore a =-6 \times 2=-12 ms ^{-2}$
$\therefore$ retardation $=12 ms ^{-2}$
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Concepts Used:
Acceleration
In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration.
