Two trains A and B of length 400 m each are moving on two parallel . . .

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 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 ?

Doubt by Ishmeet

Solution : 

Length of Train A and B = L = 400 m 
Initial velocity of both trains (u) 
=72 km/h 
= 72×(5/18) 
= 20 m/s

Train A is moving with constant velocity while the train B is accelerates with a=1 m/s².

Time of overtaking Train A by Train B  = 50 sec

Distance covered by Train A in 50 sec

s=ut+½at²
s_A=20(50)+½(0)(50)²
s_A=1000 + 0
s_A=1000 m/s

Distance covered by Train B in 50 sec

s=ut+½at²
s_B=20(50)+½(1)(50)²
s_B=1000 + 2500/2
s_B=1000 +1250
s_B=2250 m 

Distance between the two trains
=s_B-s_A
=2250 m - 1000 m 
= 1250 m

Hence the original distance between them was 1250 m. 

Note : This distance is actually the actually distance between the drivers of the two trains. If the question ask for the distance between the driver of one train back of the other train then the distance covered by the train B must be equal to Length of train B + Distance between the two trains (Driver of Train B and Gurad of Train A)+ Length of Train A

s_B=400+x+400
1250=800+x
x=1250-800
x=450 m 

Hence, the original distance between the driver of train B and Gurad of Train A would be 450 m.