Two trains A and B are moving on two parallel tracks with uniform spee

1.	Two trains A and B are moving on two parallel tracks with uniform speed of 20ms-1 in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by 1 ms-2. After 50 seconds, they are moving together, find the original distance of separation.
Answer» Initially, both A and B are moving with the same velocity in the same direction, ∴ The initial relative velocity . u_AB = u_A– u_B= 0 when t = 50 s, relative acceleration = a_AB = 1 ms^-2 If s is the distance moved, then From s = ut + 1/2at² S = u_AB × t + 1/2 a_ABt² S = 0 × t + 1/2 × 1 × 50² = 2500/2 = 1250 m. Hence, the Initial distance of separation is 1250m.

Two trains A and B are moving on two parallel tracks with uniform speed of 20ms-1 in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by 1 ms-2. After 50 seconds, they are moving together, find the original distance of separation.

Answer»

Initially, both A and B are moving with the same velocity in the same direction,

∴ The initial relative velocity .

u_AB = u_A– u_B= 0

when t = 50 s,

relative acceleration = a_AB = 1 ms^-2

If s is the distance moved, then

From s = ut + 1/2at²

S = u_AB × t + 1/2 a_ABt²

S = 0 × t + 1/2 × 1 × 50²

= 2500/2 = 1250 m.

Hence, the Initial distance of separation is 1250m.