Help on physics car project

The project is to build a little car to crash head-on into another. The car that ends up nearest the middle wins.

I'm thinking of making the wheels stop the moment it crashes so it won't be pushed back.

Should I put a cover in front that when it crashes the cover will touch the wheels and provide friction?
Or maybe "lock-in" the wheels in place? How?

I'm guessing that this contest is to see who can make the most elastic bumper, hence cushioning the blow the best, but I think your idea of locking the wheels is genius. If that is allowed, go with that.
Another option:
Have the wheels raise the car up on loose lever arms, so at the crash your car is pushed back with the lever arms rotating so the car is no longer above the wheels, instead it falls on it's belly which has a sticky surface under it