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A particle located at x = 0 at time t = 0, starts moving along with the positive x-direction with a velocity v = α√x. The displacement of the particle varies with time as

1. t²
2. t
3. t^(1/2)
4. t³

Correct answer: t²

Solution

From v = dx/dt = a*sqrt(x): integral dx/sqrt(x) = integral a dt gives 2*sqrt(x) = a*t, so x = a^2*t^2/4. Displacement varies as t^2.

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