Question

A train is moving with uniform acceleration. The two ends of the train pass through a point on the railway track with velocity v1 and v2. With what velocity the middle point of the train would pass through the same point.?

Answer 1

Let the total length of train = S
Since V1 = front end velocity , and V2 = rear end velocity

(Here Lets take V1 = u
and V2 = v for simplicity)

Uniform Acceleration of train = a m/s²
From eqn of motion ( when whole train just crosses the pole )

v² = u²+ 2aS
aS = (v² – u²)/2

Suppose v’ be velocity when half the train crosses the pole

v’² = u²+ 2aS/2
v’²= u² + aS
= u² + (v² – u²)/2

v’²= (v²+u²)/2

Now we can substitute V2 for V and V1 for u