# Collision of 2 trains and stopping distances

Two trains are driving towards each other .One at 144 km/h and the other at 72 km/h When they see each other they start to brake at 1 m/s2. There is 950m between them.

Will they hit each other or will they stop in time?

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#### Solution Preview

See the attached file.

We will start by drawing a diagram depicting the scene with the two trains heading towards each other but breaking with a de-acceleration of 1 m/s^2

{SEE ATTACHMENT FOR THE DIAGRAM}

As the velocities quoted are in Km/h and the de-acceleration is in m/s^2 and the distance quoted is in m we should first convert those velocities into m/s equivalents

So

V1 = 144 Km/h = 1.44 x 105 /3600 = 40 m/s

V2 = 72 Km/h = 7.2 x 104 /3600 ...

#### Solution Summary

A question is posed where two trains travelling in opposite directions and known speeds first see each other then start to brake. Based on the known initial speeds and the distance between the trains linear kinematics is used to determine whether the 2 trains will collide or not. Constant braking de-acceleration is assumed at 1 m/s2.