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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.?

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Solution

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

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