Question:
Two trains A and B of length 400m each are moving on two parallel tracks with uniform speed of 72km/hr in the same direction with A ahead of B . The driver of B decides to overtake A and accelerates by 1m/s2 . If after 50sec the guard of B just rushes past the driver of A. What was the original distance between them ?
Answer:
For train A:
Initial velocity, u = 72 km/h = 20 m/s
Time, t = 50 s
Acceleration, aI = 0 (Since it is moving with a uniform velocity)
From second equation of motion, distance (sI)covered by train A can be obtained as:
s = ut + (1/2)a1t2
= 20 × 50 + 0 = 1000 m
For train B:
Initial velocity, u = 72 km/h = 20 m/s
Acceleration, a = 1 m/s2
Time, t = 50 s
From second equation of motion, distance (sII) covered by train A can be obtained as:
sII = ut + (1/2)at2
= 20 X 50 + (1/2) × 1 × (50)2 = 2250 m
Length of both trains = 2 × 400 m = 800 m
Hence, the original distance between the driver of train A and the guard of train B is 2250 - 1000 - 800 = 450m.
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