Question

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 1.05 m/s2. The train on the right accelerates leftward at 0.93 m/s2.
(a) How far does the train on the left travel before the front ends of the trains pass?
(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?

Answer 1

The distance covered is 50 m, so let the rightmost train go x meters, the left goes 50-x m in the same time...

x=1/2 aright*time^2
50-x=1/2 aleft*time^2

divide the equations

x/(50-x)=aright/aleft

solve for x (right), and 50-x (left)

b. now, the distance apart the ends starts at 350m.

one goes y, the other 350-y
solve it again, only this part find the time.