# What is velocity with which the middle point of a train passes certain point?What is velocity with which the middle point of a train passes certain point if the ends of the train which moves with...

What is velocity with which the middle point of a train passes certain point?

What is velocity with which the middle point of a train passes certain point if the ends of the train which moves with constant acceleration pass the certain poin with velocities u and v?

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### 1 Answer

Since the problem provides the velocities of the ends of train when they pass through the indicated point, you should use the following relation that relates these velocities, acceleration and the distance travelled such that:

`u^2 - v^2 = 2*a*d =gt a = (u^2 - v^2)/(2d)`

The problem requests the velocity of the middle point of the train when it passes through the indicated point.

`u^2 - v^2 = 2*a*(d/2) =gt u^2 - v^2 = a*d =gt a = (u^2 - v^2)/d`

Since the problem provides the information that the acceleration is constant,yields:

`u^2 = v^2 + (u^2 - v^2)/2 =gt u^2 = (v^2 + u^2)/2`

`u = sqrt((v^2 + u^2)/2)`

**Hence, evaluating the velocity of the middle point that passes through the indicated point yields `u = sqrt((v^2 + u^2)/2).` **