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  4. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:

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Q. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u $ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is:

JEE MainJEE Main 2021Motion in a Straight Line

Solution:

$\left( v ^{\prime}\right)^{2}= u ^{2}+2 ad$
$v ^{2}=\left( v ^{\prime}\right)^{2}+2 ad$
solving, we get
$v^{\prime}=\sqrt{\frac{v^{2}+u^{2}}{2}}$
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