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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 BYJU'S Exam Prep
Updated on: September 25th, 2023
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.