A boat of mass $300 k g$ moves according to the equation $x = 1.2 t^{2} - 0.2 t^{3}$ . When will the force become zero?

2 s

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1 s

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6 s

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2.8 s

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Solution

The correct option is B $2 s$
According to first law of Newton's, force will become zero when a body move with constant speed or with zero acceleration. So,
$x = 1.2 t^{2} - 0.2 t^{3}$
$⟹ \frac{d x}{d t} = 2.4 t - 0.6 t^{2}$
$⟹ \frac{d^{2} x}{d t^{2}} = 2.4 - 1.2 t = 0 \Rightarrow t = 2 s$

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