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 $'S'$ be the distance between two ends $'a'$ 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, $V^{2}_{c}-u^{2}=2a \frac{S}{2}$
$V^{2}_{c}=u^{2}+aS$
$V^{2}_{c}=u^{2}+\frac{V^{2}-u^{2}}{2}$
$V_{c}=\sqrt{\frac{u^{2}+v^{2}}{2}}$