Question

A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard’s room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.

• A. $\frac{u+v}{2}$
• B. $\frac{1}{2}\sqrt{u^2+v^2}$
• C. $\sqrt{uv}$
• D. $\sqrt{\left(\frac{u^2+v^2}{2}\right)}$

Answer 1

Answer: (D)

Let ${}^{\prime }{S}^{\prime }$ be the distance between two ends ${}^{\prime }{a}^{\prime }$ be the constant acceleration
As we know $V^2-u^2=2aS$
or, $aS=\frac{V^2-u^2}{2}$
Let $V$ be velocity at mid point.
Therefore, $V_c^2-u^2=2a\frac{S}{2}$
$V_c^2=u^2+aS$
$V_c^2=u^2+\frac{V^2-u^2}{2}$
$V_c=\sqrt{\frac{u^2+v^2}{2}}$