# Kinematics problem (one dimension)

Hello,

I am a tenth-grader physics student, and I have a mechanics-realted problem you may think is quite trivial, but I have been unsuccessfully trying to solve it for a whole day, so I would thank you if you answered.
Please consider the attached graph; the question relates to it:
Two trains, a red one and a yellow one, travel towards each other on a straight railway-track. When the distance between them is 800 m, the drivers notice the danger and hit the brakes simultaneously. The graph shows their velocity in respect to time from the moment of hitting the brakes, if each train had travelled alone.
(Here there are a couple of pretty eaay questions; I'm skipping right to the problem.)
Did the trains collide into each other? If they did – when did it happen? And if the didn't – what was the distance between them when they stopped?
The other attached image shows my feeble attempts to solve this question.
The last thing I should do about these trains is draw (on the same coordinate system) a schematic displacement-time graph for both trains from t=0 to the moment of stopping/collision.

Attachments:
Image 1 (the calculations) - http://img468.imageshack.us/img468/2295/trains1dy3.jpg [Broken]
Image 2 (the graph) - http://img157.imageshack.us/img157/200/trains2ab7.jpg [Broken]

P.S: I just noticed a couple of small alignment problems in Image 1. I'm sorry about them, I think my OpenOffice needs a bit of configuration.

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