# Train Collision Problem

1. Sep 18, 2007

### SharkFin39

1. The problem statement, all variables and given/known data

Two trains, one traveling at 74.00 km/h and the other at 148.00 km/h, are headed toward one another along a straight, level track. When they are 938 m apart, each engineer sees the other's train and applies the brakes. The brakes decelerate each train at the rate of 1.0 m/s2. Is there a collision? What distance do the trains need to allow between them to stop at this acceleration? What acceleration do the two trains need to have to stop exactly in a distance of 938 m?

2. Relevant equations

V^2 - Vo^2 = 2a(X-Xo) (this is what I used to solve parts 1 and 2)

3. The attempt at a solution

Well, I had no problem with the first two parts of the question. Using the above formula I determined that the first train needed 211.275m to stop, and the second needed 845.057m to stop. They needed a total distance of 1056.332m to stop, therefore there was a collision.

My question is how would I go about solving the third part of the question. The question calls for a single answer in m/s^2. Otherwise, I would've just divided the 938m by 2, and solved for two seperate accelerations. I think I'm actually more stumped by the question than the calculations. If this makes sense to anyone, I'd really appreciate some guidance. Thank you in advance for you assistance.

SharkFin

2. Sep 18, 2007

### mgb_phys

Use s=ut + 1/2 at^2 for each train and the 's' from both trains must add to 938m

3. Sep 18, 2007

### neutrino

For the last question, consider just one train at a time. If the train 1 travelling at 74kmph was 938m away from some point (call it A), what should its deceleration be so that it comes to rest at A. Similarly for the other train.

4. Sep 18, 2007

### D H

Staff Emeritus
This won't work, for two reasons. (1) He is looking for a single number, not two numbers, and (2) the trains will crash.

The two trains have some common breaking deceleration. Call this "a". Train 1 will come to a stop after traveling some distance d1, train 2 after some distance d2. You don't know what d1 and d2 are, but you do know what they are in terms of "a" and you do know their sum.

5. Sep 5, 2008

### southernjeepn

V^2 - Vo^2 = 2a(X-Xo) (this is what I used to solve parts 1 and 2)
Sharkfin. I have a very similar problem. Almost exactly but can not get your answers for x of each train's distance to stop to save my life. You converted km/h to m/s I'm pretty sure. What did u plug into each variable for that equation. a=-1.0, V=0?, Vo=74 km/h? (convert), X=?, Xo=?. Are u using X=938, Xo=unknown, V=0 (bc it stopped), Vo=20.56 m/s (after conversion), Having a hard time figuring out where the initial variables plug into the equation