Two trains face each other on adjacent tracks. they are initially at rest, and their front ends are 50 m apart. the train on the left accelerates rightward at 1.15 m/s2. the train on the right accelerates leftward at 1.15 m/s2. (a) how far does the train on the left travel before the front ends of the trains pass? 25 m (b) if the trains are each 150 m in length, how long after the start are they completely past one another, assuming their accelerations are constant?

(a) d' = 22.73 m

(b) t = 13.187 s

Solution:

As per the question:

Initial speed of both the trains, u = 0 m/s

The distance between the front ends of the train, d = 50 m

Acceleration of the train on the left, towards right

Acceleration of the train on the right, towards left

Relative acceleration of the train ,

Now,

(a) Using the eqn (2) of motion, for the train on the left:

Now, the distance covered by the train on the left before passing the front end:

d' = 43.073 m

d' = 43.073 - 25 = 22.73 m

(b) Now,

Acceleration is constant at

Length of the trains, l = 150 m

Total distance, D = l + d = 150 + 50 = 200 m

Now, from eqn (2) of motion again:

200 = 0.t +

t = 13.187 s

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