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Non Uniform Motion & Avg Velocity

The position ...

Question

The position $x$ of a particle varies with time $(t)$ as $x = a t^{2} - b t^{3}$ . The acceleration at time $t$ of the particle will be equal to zero, where $t$ is equal to

\frac{2 a}{3 b}

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\frac{a}{b}

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\frac{a}{3 b}

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zero

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Solution

The correct option is D $\frac{a}{3 b}$
$x = a t^{2} - b t^{3}$
Velocity = $\frac{d x}{d t} = 2 a t - 3 b t^{2}$
and acceleration = $\frac{d^{2} x}{d t^{2}} = 2 a - 6 b t$
Acceleration will be zero if
$2 a - 6 b t = 0 \Rightarrow t = \frac{2 a}{6 b} = \frac{a}{3 b}$

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