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, $v^2-u^2=2as$ $v^2-{60}^2=2a\times \frac{700}{a}$ $=1400$ $v^2=1400+3600$ $v=\sqrt{5000}$ $=70.7km{h}^{-1}$