Please show all work and no textbook solutions Please do not

Please show all work and no textbook solutions. Please do not attempt if you don\'t understand entire problem, THANK YOU!

Train A with proper length L moves eastward at speed v, while train B with proper length 2L moves westward also at speed v. How much time does it take for the trains to pass each other (defined as the time between the fronts coinciding and the backs coinciding): (a) In A’s frame? (b) In B’s frame? (c) In the ground frame? (d) Verify that the invariant interval is the same in all three frames.

Solution

for frame A:

In the frame of A speed of B is 2v and the total distance to travel is 3L
thus, the time is,

         time = 3L/2v

for frame B:

In the frame of B speed of A is 2v
hence, the time t is,

           time = 3L/2v

for ground\":

In the frame of ground, the time is,

    time = 3L/2v

(d)

time taken is irrespective of the frame. so, the time is same in all frames.