The second paragraph seems to be asking about some physics-based appoach for powering the car, and driving it for 1 meter (at least); and asking for some other aspects of the model-car design that is based on physics-knowledge.
The first part can be the conceptual design of the car. And the second part can be more related to the detail design of the car.
Conceptually, the car can be driven by the following methods, where energy is not coming from batteries or electricity.
- Mechanical power: gears and springs that can be found in toy-cars.
- inertia release: based on Newton's laws, something (fluid, or balls) can be released towards the rear of the car, to move the car forward. You could design a simple mechanism (e.g. 1 Liter of pet bottle with a hole at the rear-bottom-corner, throwing the liquid towards the back of the car). or some other mechanism, that releases a few balls by the help of gravity towards the back. Gravity can be used to pull the balls downwards, and some sloped-road can be built to guide them towards the back.
- chemical reaction: soda + Mentos, kind of rocket science, but the force is good. although not much computable beforehand and more of a quick-explosion rather than a slow and adjustable thrust.
After the conceptual design, other physical knowledge comes into play. But that depends on the conceptual design, and there are possibly tens or hundreds of physical relationships and dependencies between the selected design features, design characteristics, materials and the overall performance of the vehicle. Most importantly, weight of the car and the main friction (tire-ground, or inter-mechanism friction) will play a huge role.
If you edit your question to give more details, and maybe with some sketches of your possible design, we could elaborate more on this interesting and thought provoking project.