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2.Motion in Straight Line
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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
A
$\sqrt{\frac{ v ^{2}+ u ^{2}}{2}}$
B
$\frac{ v - u }{2}$
C
$\frac{ u + v }{2}$
D
$\sqrt{\frac{ v ^{2}- u ^{2}}{2}}$
(JEE MAIN-2021)
Solution
$\left( v ^{\prime}\right)^{2}= u ^{2}+2 ad$
$v ^{2}=\left( v ^{\prime}\right)^{2}+2 ad$
solving, we get
$v^{\prime}=\sqrt{\frac{v^{2}+u^{2}}{2}}$
Standard 11
Physics
