I'm also doing this competition this year. Our problem so far seems to be that we don't have an electrical engineering program at my school, it's mostly all MEs and IEs, so although electronics aren't out of the picture, it's going to take a lot more effort to get them to work.

You can look into CO2 cars, there are quite a few on youtube. They're fast as hell although you'd have to design the triggering mechanism to be on the car and travel with it.

For general triggering mechanism's, you can do something like theholymac was talking about with reed switches or even a wide bar that presses a small button when it gets hit. You may also want to look into 555 timing circuits so that a battery powered car for instance will only run for so long before it shuts off again. I don't know how much of a problem this will be for you or us though.

You may also want to look into very small but high 'C' value lithium batteries. A single car only needs to run for a few seconds, but may also pull >5 amps at 11V or higher. I was surprised how small a battery can be and still be able to provide that power. From what a gathered, you can get a 350mah battery that is about the size of your thumb, except thinner, but pull 10 amps off of it. And it's not even really expensive!

I haven't looked into it but maybe a clockspring driving a gearset would work well, but i don't know if a good sized one could easily be had.

We're all really in just the brainstorming stage right now though, nothing has actually been tried yet.

We do have a 'topsecret' build though. It's quite an odd contraption so it'll be interesting to see if it'll work. I'll have to make a post about it when we get it built.

-Good luck!