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Q.

An engine of a train, moving with uniform acceleration, passes the signal post with velocity ‘U’ and the last compartment with velocity ‘V’. The velocity with which middle point of the train passes the signal post is

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a

$\frac{V - U}{2}$

b

$\sqrt{\frac{V^{2} - U^{2}}{2}}$

c

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

d

$\sqrt{\frac{V^{2} + U^{2}}{2}}$

answer is D.

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Detailed Solution

$V^{2} - U^{2} = 2 aS$

$\Rightarrow V^{2} - U^{2} \propto S$

Let ‘l’ be the length of the train.

$\frac{l}{I / 2} = \frac{V^{2} - U^{2}}{V_{1}^{2} - U^{2}} \Rightarrow V_{1} = \sqrt{\frac{V^{2} + U^{2}}{2}}$

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An engine of a train, moving with uniform acceleration, passes the signal post with velocity ‘U’ and the last compartment with velocity ‘V’. The velocity with which middle point of the train passes the signal post is