A train is moving along a straight path with uniform acceleration. Its engine passes across a pole…

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

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