The motion of a particle along a straight line is described by equation : `x = 8 + 12 t - t^3` where `x` is in metre and `t` in second. The retardation of the particle when its velocity becomes zero is.A. (a) ` 24 m//s^2`B. (b) ` zero`C. (c ) ` 6 m//s`D. (d) ` 12 m//s^2`

The motion of a particle along a straight line is described by equatio

1.	The motion of a particle along a straight line is described by equation : `x = 8 + 12 t - t^3` where `x` is in metre and `t` in second. The retardation of the particle when its velocity becomes zero is.A. (a) ` 24 m//s^2`B. (b) ` zero`C. (c ) ` 6 m//s`D. (d) ` 12 m//s^2`
Answer» Correct Answer - (d) Here, ` x = 8 + 12 t-t^3` :. ` When velocity is zero (v=0) . The ` 12 -3 t^3 =0 ` or ` 12 =3 t^2 ` or t^2 =4` :. ` t=2 s` Also, ` a= (dv)/(dt) = d/(dt) (12 -3 t^2) =- 6t` At ` t= 2 s a =- 6 t =- xx 2 =- 12 m//s^2` So retardation is ` 12 m//s^(2)`.

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The motion of a particle along a straight line is described by equation : `x = 8 + 12 t - t^3` where `x` is in metre and `t` in second. The retardation of the particle when its velocity becomes zero is.A. (a) ` 24 m//s^2`B. (b) ` zero`C. (c ) ` 6 m//s`D. (d) ` 12 m//s^2`

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