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The two ends of a train moving with unif...

The two ends of a train moving with uniform acceleration pass a certain point with velocity u and v. Find the velocity with which the middle point of the train passes the same point.

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Between `A, B:(v^(1))^(2)-u^(2)=2as//2`
Between `B,C:v^(2)-(v^(1))^(2)=2as//2`
`implies (v^(1))^(2)-u^(2)=v^(2)-v^(12)`
`2(v^(1))^(2)=v^(2)+v^(2)`
Velocity at mid point is `v^(1)=sqrt((u^(2)+v^(2))/(2))`
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