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Spring Force

The position ...

Question

The position $x$ of a particle varies with time $t$ as $a t^{2} - b t^{2}$ . The acceleration of the particle be $0$ at time $t$ equals to

\frac{a}{b}

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\frac{2 a}{3 b}

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\frac{a}{3 b}

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zero

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Solution

The correct option is C $\frac{a}{3 b}$
$\begin{matrix} x = a t^{2} - b t^{3} v = \frac{d x}{d t} = 2 a t - 3 b t^{2} a = \frac{d v}{d t} = 2 a - 6 b t = 0 ∴ t = \frac{a}{3 b} \end{matrix}$
Hence, Option $C$ is correct answer.

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