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For a particle undergoing rectilinear motion with uniform acceleration, the magnitude of displacement is one third the distance covered in some time interval. The magnitude of final velocity is less than magnitude of initial velocity for this time interval. Then the ratio of initial speed velocity to the final speed for this time interval is:

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$\sqrt{3}$

$\sqrt{2}$

answer is A.

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Detailed Solution

Let u and v denote initial and final velocities. The nature of motion is indicated in diagram.

Hence initial and final speeds are given by equation

$0^{2} = u^{2} - 2 a \times 2 S and v^{2} = 0^{2} + 2 as$

$∴ v = \frac{u}{\sqrt{2}} or \frac{u}{v} = \sqrt{2}$

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