question_answer

A train is moving along a straight path with uniform acceleration. Its engine passes across a pole with a velocity of 60 km/h and the end (guard's van) passes across same pole with a velocity of 80 km/h. With what velocity does the middle part of the train pass the same pole.

Answer:

Let s be length of train, t be time taken by full train to cross the pole and a be uniform acceleration of train. from,\[{{v}^{2}}-{{u}^{2}}=2as,\frac{{{80}^{2}}-{{60}^{2}}}{2a}=s\] or \[s=\frac{6400-3600}{2a}=\frac{1400}{a}\]                       ….(1) The middle part of the train covers half the total distance,\[s/2=\frac{700}{a}\] From,\[{{v}^{2}}-{{u}^{2}}=2as,\,\,{{v}^{2}}-{{60}^{2}}=2a\times \frac{700}{a}=1400\] \[{{v}^{2}}=1400+3600=\sqrt{5000}=70.7\,km/h.\]