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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

1. √((v² + u²)/2)
2. (v − u)/2
3. (u + v)/2
4. √((v² − u²)/2)

Correct answer: √((v² + u²)/2)

Solution

With uniform acceleration, v^2 = u^2 + 2aL over the full train. At the midpoint: v_mid^2 = u^2 + 2a(L/2) = u^2 + (v^2 - u^2)/2 = (u^2 + v^2)/2, so v_mid = sqrt((u^2 + v^2)/2).

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