# Two trains A and B lengths 400 m each are moving on two parallel tracks with a uniform speed of 72 km/h 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?

By Ritesh|Updated : November 14th, 2022

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, the original distance between them is 1250 m. Steps to find the original distance between A and B train:

Step 1: It is given that:

length of train A = Length of train B = 400m

Also given that the Initial velocity (uA) of train A = Initial speed of train B (uB)

Therefore:

uA = uB = 72 km/h = 72 x 5/18 m/s = 20 m/s

In front of the train, B is train A.

Acceleration in train B (aB) = 1m/s2

time(t) = 50 sec

Step 2: Calculating the initial separation between trains A and B:

The formula for train B's relative velocity to train A is:

uBA = uB - uA

Substituting the values we get:

uBA = 20 m/s - 20 m/s

We get

uBA = 0

The second equation of motion determines the distance travelled by train B with regard to train A in the specified amount of time:

s = ut + ½ at2

Let The distance that train B must travel to simply cross-train B is shown by the symbol sBA:

We obtain: by putting the values:

sBA = uBA x t + ½ at2

Substituting the values we get:

sBA = 0 x 50 sec + ½ x 1 m/s2 x (50 sec)2

sBA = 25 x 50

sBA = 1250 m

Original distance between the train = Distance covered by train B with respect to training A to just cross-training A (sBA)

= 1250 m

Therefore, the original distance between them is 1250 m.

Summary:

## Two trains A and B lengths 400 m each are moving on two parallel tracks with a uniform speed of 72 km/h 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?

Two trains A and B lengths 400 m each is moving on two parallel tracks with a uniform speed of 72 km/h 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, the original distance between them is 1250 m.