The motion of a particle along a straight line is described by equation $x = 12 t - t^{3}$ where $x$ is in meter and $t$ is in second. The time instant when velocity of the particle becomes zero is

2 s

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1 s

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4 s

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3 s

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Solution

The correct option is A $2 s$
The position of the particle is given by
$x = 12 t - t^{3}$
$∵ v = \frac{d x}{d t}$
$∴ v = 12 - 3 t^{2}$
$\Rightarrow t^{2} = 4$ (For $v = 0$ )
$\Rightarrow t = 2 s$

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The correct option is A $2 s$
The position of the particle is given by
$x = 12 t - t^{3}$
$∵ v = \frac{d x}{d t}$
$∴ v = 12 - 3 t^{2}$
$\Rightarrow t^{2} = 4$ (For $v = 0$ )
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