Kinematics Question 378
Question: A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. it’s 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.
Options:
A) $ \frac{\text{u+v}}{2} $
B) $ \frac{1}{2}\sqrt{{{u}^{2}}\text{+}{{v}^{2}}} $
C) $ \sqrt{uv} $
D) $ \sqrt{( \frac{{{u}^{2}}+{{v}^{2}}}{2} )} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let ‘S’ be the distance between two ends ‘a’ be the constant acceleration.
As we know $ {{v}^{2}}-{{u}^{2}}\text{=2aS or, aS=}\frac{{{v}^{2}}-{{u}^{2}}}{2} $ .
Let v be velocity at mid-point.
Therefore, $ v _{c}^{2}-{{u}^{2}}\text{=2a}\frac{S}{2}\Rightarrow v _{c}^{2}\text{=}{{u}^{2}}\text{+aS} $
$ v _{c}^{2}={{u}^{2}}+\frac{{{v}^{2}}-{{u}^{2}}}{2}\Rightarrow {{v} _{c}}=\sqrt{\frac{{{u} _{2}}\text{+}{{v}^{2}}}{2}} $ S
