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=3.2 m/s. The second train starts from rest at some unknown positive x position D, and accelerates with a2=-0.43 m/s2 . The trains collide in a time t=25 s. Find the distance D.

Answer 1

Since both trains collides after time 't' , So total distance traveled by both trains will be D. So

D = |d1| + |d2|

|d1| = distance traveled by 1st train moving at constant velocity = Speed*time = v1*t

|d2| = distance traveled by 2nd train moving in opposite direction of train 1

from 2nd kinematic equation:

|d2| = v2*t + (1/2)*a2*t^2, since v2 = 0 m/s, So

D = |d1| + |d2|

D = v1*t + (1/2)*a2*t^2

D = 3.2*25 + (1/2)*0.43*25^2

D = 214.375 m

D = distance traveled by both trains = Initial position of 2nd train = 214.4 m

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