Question

The two ends of a train moving with a constant acceleration pass a certain point with velocities u and v. What is the velocity with which the middle point of the train passes the same point?

Answer 1

Let the length of the train be ‘L’.

As it crosses the point, the initial velocity can be taken as ‘u’ and final velocity as ‘v’.

So, v² = u² + 2aL

=> v² – u² = 2aL ……………(1)

Suppose the velocity with which the midpoint crosses that certain point be v^/. In this case the distance traveled is L/2.

So,

(v^/)² = u² + 2a(L/2)

=> (v^/)² = u² + ½ × (v² – u²) [using (1)]

=> (v^/)² = (v² + u²)/2

=> v^/ = {(v² + u²)/2}^1/2

This is the velocity of the midpoint of the train with which it crosses that point.