Question 35 of 308

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$\dfrac{u+v}{2}$B$\sqrt{\dfrac{{v}^{2}+{u}^{2}}{2}}$C$\dfrac{v-u}{2}$D$\sqrt{\dfrac{{v}^{2}-{u}^{2}}{2}}$

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Answer: (B) $\sqrt{\dfrac{{v}^{2}+{u}^{2}}{2}}$

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