Question

Two extreme ends of a moving train (engine and guard coach) pass a pole with speed $u$ and $v$ respectively with a constant acceleration. The speed with which the middle point of the train will pass the same pole is

• A. $\frac{u+v}{2}$
• B. $\frac{v^2+u^2}{2}$
• C. $\frac{uv}{2}$
• D. $\sqrt{\frac{u^2+v^2}{2}}$

Answer 1

The correct option is D $\sqrt{\frac{u^2+v^2}{2}}$

From third equation of motion $v^2–u^2=2as$
From the given question, we can infer that the initial velocity of the train was $u$ and final velocity is $v$.
Therefore acceleration of the train if length of train is $l$ is $a$ = $\frac{v^2–u^2}{2l}$
When the middle part of the train passes the pole, the trains has displaced by $l/2$, then
let $V$ be the velocity of the middle then using the third equation of motion we get,
$V^2=u^2+2a\frac{l}{2}$
Now, substituting value of a here we get,
V = $\sqrt{\frac{u^2+v^2}{2}}$
Therefore, option D is correct.