Question

Two trains are on a collision course along the x axis. The first train starts at the origin and moves with constant velocity v₁=3.7 m/s. The second train starts from rest at some unknown positive x position D, and accelerates with a₂=-0.79 m/s² . The trains collide in a time t=28 s. Find the distance D.

Answer 1

The first train starts from the origin.
The collision happens at the time t = 28 s
The distance travelled by the first train before the collision
d = v1 x t = 3.7 m/s x 28 s = 103.6 m
The second train starts from rest at an unknown position D.
The distance travelled by the second train before colliding with the first train.
S = u t + (1/2) a t2
We can find the distance travelled by the second train within the time t = 28 s
a = - 0.79 m/s2
u = 0 m/s
The initial position is D. Let S be the final position. We know that the final position is 103.6 m, measured along the positive x-axis.
103.6 = D + (1/2) x -0.79 m/s2 x (28 s)2
D = 103.6 + 309.68
D = 413.28 m