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.

Explanation

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