Q: 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. The middle point of the train will pass across same pole with a velocity:
(a) 70 km/h
(b) 70.7 km/h
(c) 65 km/h
(d) 75 km/h
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Ans: (b)
Sol: Let S = length of train,
t = time taken by full train to cross the pole,
a= uniform acc. of train.
From v2 = u2 + 2 a S
S = v2 – u2/2a
S = 802 – 602/2a
S = 1400/a
The middle point of the train is to cover a distance is
S’ = S/2 = 700/a
From v2 = u2 + 2 a S’
v2 = 602 + 2 a (700/a)
v2 =1400 + 3600
$ \displaystyle v = \sqrt{5000}$
v = 70.7 km/h