A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on…
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.
$\frac{u+v}{2}$
$\frac{1}{2} \sqrt{u^2+v^2}$
$\sqrt{u v}$
$\sqrt{\left(\frac{u^2+v^2}{2}\right)}$
Solution
Let ' $S$ ' be the distance between two ends ' $a$ ' be the constant acceleration As we know $V^2-u^2=2 a S$
or, $a S=\frac{V^2-u^2}{2}$
Let $V$ be velocity at mid point.
Therefore, $V_c^2-u^2=2 a \frac{S}{2}$
$
\begin{aligned}
& V_c^2=u^2+a S \\
& V_c^2=u^2+\frac{V^2-u^2}{2} \\
& V_c=\sqrt{\frac{u^2+v^2}{2}}
\end{aligned}
$