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 v^{2} = u^{2} + 2 a S

S = v^{2} – u^{2}/2a

S = 80^{2} – 60^{2}/2a

S = 1400/a

The middle point of the train is to cover a distance is

S’ = S/2 = 700/a

From v^{2} = u^{2} + 2 a S’

v^{2} = 60^{2} + 2 a (700/a)

v^{2} =1400 + 3600

$ \displaystyle v = \sqrt{5000}$

v = 70.7 km/h