Make your own friction driven car. This kit includes a motor and all the stuff you need to mount an engine to a wood chassis. It's up to you to decide how the engine works and drives the wheels. It is a great problem solving exercise.
The kit includes a battery holder, but you need to supply the 1-AA battery to power the motor. As a change up you can substitute a 1000 mAmp solar cell! For ages 12 and up.