The two ends of a train moving with uniform acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is:
Since the train has uniform acceleration, we know,
v2=u2+2 al ( l=length of train ),
so the acceleration of the train can be found out using this, so, a =v2−u22l.
For the central point to find the velocity:
s or the displacement will be half the length of the train that is 'l' at the midpoint and velocity at the midpoint will be vm.