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A particle located at x = 0 at time t = 0,starts moving along the positive, x-direction with a velocity 'v' that varies as $v = α \sqrt{x}$ ,. The displacement of the particle varies with time as:

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t^1/2

t²

t³

answer is C.

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Detailed Solution

As $v \propto \sqrt{x} or v^{2} \propto x \Rightarrow$ constant acceleration ( $∵ v^{2} = u^{2} + 2 ax, u = 0$ ).
Therefore, displacement $\propto t^{2} (∵ {II}^{nd} eq . of motion s = ut + \frac{1}{2} {at}^{2})$

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