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Class 11
Physics
Motion in a straight Line
two trains a and b of length 400 m each are moving...

Question:
Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h^–1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s². If after 50 s, the guard of B just brushes 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, a_I = 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_I = ut + ½ a_It²

= 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:

s_Il = ut + ½ at²

= 20 x 50 x ½ x 1x (50)² = 2250 m

Hence, the original distance between the driver of train A and the guard of train B

= 2250 –1000 = 1250 m.

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