a goods train accelerating uniformely on a straight railway track, approaches an electric pole standing on the side of track, it’s engine passes the pole with velocity “u” and the gaurd’s room passes with velocity “V” then middle wagon of the train passes the pole with a velocity

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$\frac{1}{2} \sqrt{u^{2} + V^{2}}$

$\frac{u + V}{2}$

$\sqrt{u V}$

$\sqrt{[\frac{u^{2} + V^{2}}{2}]}$

answer is D.

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Detailed Solution

Let “s” be the distance between two ends of train, ‘a’ is constant acceleration

$V^{2} - u^{2} = 2 a s, a s = \frac{V^{2} - u^{2}}{2}$

Let $V_{C}$ be velocity at midpoint

$∴ V_{_{C}}^{2} - u^{2} = \frac{2 a s}{2}$

$V_{_{C}}^{2} = \frac{V^{2} - u^{2}}{2} + u^{2}$

$V_{_{C}}^{} = \sqrt{\frac{V^{2} + u^{2}}{2}}$

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