Question

Two trains a & b 100 km apart are travelling towards each other on different tracks with starting speed of 50 km/h for both. the train a accelerates at 20 km/h2 and the train b retards at the rate 20 km/h2 . the distance covered by the train a when they cross each other is

Answer 1

The position of train a as a function of time is:

 a(t) = v0 t + 1/2 at^2

  Likewise for train b

 b(t) = d0 - v0 t + 1/2 at^2

  At crossing,

 a(t) = b(t)

  Notice that the accelerations are actually equal and in the same direction, so they don't matter a bit when it comes to determining WHEN the collision happens--they cancel right out. So you solve for the crossing time:

 t = d0 / 2v0

  And the position of a is:

 a(d0/2v0) = d0/2 + 1/8 a(d0/v0)^2

  They give you the distance between trains (d0), the acceleration (a), and their initial speed (v0).