Q: 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 sec. The retardation of the particle when its velocity becomes zero, is

(a) 24 ms^{–2}

(b) zero

(c) 6 ms^{–2}

(d) 12 ms^{–2}

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Ans: (d)

Sol: $ \displaystyle v= \frac{dx}{dt} = 12 – 3t^2 $

When v= 0

t = 2 sec

Again differentiating with respect to time ,

$ \displaystyle a = \frac{dv}{dt}= -6t $

a = -12 m/s^{2}