# The motion of a particle along a straight line is described by equation : x = 8 + 12 t - t3 Where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is: Option 1) 24 ms-2 Option 2) Zero Option 3) 6 ms-2 Option 4) 12 ms-2

As we learnt in

Introduction to Differentiation -

$\frac{d}{dx}\left ( x^{n} \right )={n} x^{n-1}$

- wherein

$\frac{d}{dx}\left ( x^{5} \right )=\left ( n=5 \right )$

$\Rightarrow {n}x^{n-1}$

$\Rightarrow {5}x^{5-1}$

$\Rightarrow {5}x^{4}$

$x=8+12t-t^{3}$

$v=\frac{dx}{dt}=12-3t^{2}$

Put $v=0$            $3t^{2}=12,$            $t=2 \sec$

$a=-6 \times 2=-12m/s^{2}$

Retardation = $12m/s^{2}$

Correct option is 4.

Option 1)

24 ms-2

Incorrect

Option 2)

Zero

Incorrect

Option 3)

6 ms-2

Incorrect

Option 4)

12 ms-2

Correct

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