Distance traveled by a rubber band powered car

[Joellll]

okay guys I've been looking for ages and i just can't find anything that will help me with finding a distance that will be travel by a rubber band powered car. I've been playing around with kinetic energy= potential energy but i can't seem to get anywhere. Any help will be greatly appreciated

I found that F*d=(k*x^2)/2 so i can solve for a distance there but would that only give me the distance if i flicked the rubber band not if that band was powering the car.

 

[Livect]

The problem is that a rubber band is not hookian -- it does not exert force linearly based on the distance it's stretched. Another problem is that, assuming the car goes along a horizontal, all of the energy of the rubber band goes to kinetic, and everything ends up as friction.

I suppose you could cheat a little, and say that the number of revolutions you wound it up multiplied by the circumference of the wheel would be the distance it goes. As long as the wheels don't slip and the car stops immediately after the rubber band is completely unstretched, this would be a decent estimate.