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?

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Answer 1 · 2017-06-15T17:26:10

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

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)#