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If a particle is moving along $x -$ axis where $x$ is given as function of time as $x = t - t^{3}$ Suppose analysis of motion starts at $t = 0$ ( $x$ in meters and ' t ' is in sec) (Here velocity $= \frac{d x}{d t}$ and acceleration $= \frac{d^{2} x}{d t^{2}}$ )

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When acceleration is zero then velocity is $2 m s^{- 1}$

When velocity is zero the acceleration is $- 2 \sqrt{3} m s^{- 2}$

When acceleration is zero then velocity is $1 m s^{- 1}$

When velocity is zero the acceleration is $2 \sqrt{3} m s^{- 2}$

answer is B, C.

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Detailed Solution

$x = t - t^{3}, v = 1 - 3 t^{2}, a = - 6 t$

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