An engine of a train moving with uniform acceleration passes an electric pole with velocity u and last compartment with velocity v. The middle point of the train passes past the same pole with a velocity of?

1 Answer
Jun 15, 2017

The velocity is =sqrt((u^2+v^2)/2)

Explanation:

Let the length of the train be =l

We apply the equation of motion

v^2=u^2+2al

2al=v^2-u^2

The acceleration is a=(v^2-u^2)/(2l)

For, half the train, the length is =l/2 and the

velocity is =w

Therefore,

w^2=u^2+2a*l/2

=u^2+al

=u^2+(v^2-u^2)/(2l)*l

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

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

So,

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