Two trains A and B of length 400 m each are moving on two parallel tracks with
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 ms-2. If after 50 s, the guard of B
just brushes past the driver of A, what was the original distance between the
trains
To solve this problem, we need to break it down into steps:
Step 1: Convert the speed from km/h to m/s.
The speed of both trains is given as 72 km/h. To convert it to m/s, we divide it by 3.6 (since 1 km/h is equal to 1/3.6 m/s).
Speed = 72 km/h = (72/3.6) m/s = 20 m/s
Step 2: Calculate the acceleration of train B.
The acceleration of train B is given as 1 m/s^2.
Acceleration = 1 m/s^2
Step 3: Calculate the relative speed of train B with respect to train A.
The relative speed is the difference between the speeds of the two trains.
Relative speed = Speed of B - Speed of A
= 20 m/s - 20 m/s
= 0 m/s
Step 4: Calculate the distance covered by train B in 50 seconds.
Using the equation of motion:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Here, the initial velocity of train B is 20 m/s, time is given as 50s, and acceleration is given as 1 m/s^2.
Distance = 20 m/s * 50 s + (1/2) * 1 m/s^2 * (50 s)^2
= 1000 m + 25 m
= 1025 m
Step 5: Calculate the distance between the trains at the starting point.
Since train B just brushes past the driver of train A, the distance covered by train B is the sum of the lengths of both trains.
Distance = Length of A + Length of B
= 400 m + 400 m
= 800 m
Step 6: Calculate the original distance between the trains.
The original distance between the trains is the difference between the distance covered by train B and the distance covered by train A.
Original distance = Distance - Distance covered by B
= 800 m - 1025 m
= -225 m
Since the result is negative, it implies that train B has not yet completely overtaken train A. The original distance between the trains was 225 meters.