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,

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