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} )} $

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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



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