Question

A train is moving along a straight path with uniform acceleration. Its engine passes across a pole with a velocity of 60 $ km{{h}^{-1}} $ and the end (guards van) passes across same pole with a velocity of 80 $ km{{h}^{-1}} $ . The middle point of the train will pass across same pole with a velocity

• A. 70 $ km{{h}^{-1}} $
• B. 70.7 $ km{{h}^{-1}} $
• C. 65 $ km{{h}^{-1}} $
• D. 75 $ km{{h}^{-1}} $

Answer 1

Answer: (B)

From, $ {{v}^{2}}-{{u}^{2}}=2as $ $ \frac{{{80}^{2}}-{{60}^{2}}}{2a}=s $ $ s=\frac{6400-3600}{2a} $ $ =\frac{2800}{2a} $ $ =\frac{1400}{a} $ The middle point of the train is to cover a distance $ \frac{s}{2}=\frac{700}{a} $ From, $ {{v}^{2}}-{{u}^{2}}=2as $ $ {{v}^{2}}-{{60}^{2}}=2a\times \frac{700}{a} $ $ =1400 $ $ {{v}^{2}}=1400+3600 $ $ v=\sqrt{5000} $ $ =70.7\,km{{h}^{-1}} $