Here is the easiest design I can think of.
Here is a bit of a unoffical law in physics of this caliber we are dealing with here.(that I realized and am writing in my own words)
Changing the direction, of the trajectory, of a body of mass 90 degrees is equivalent (the same) in terms of force and momentum, as bringing an object to rest, ignoring frictions involved in that process.
So what does this mean in terms of make a car move very simple?
It means, that if you could find a 1kg ball, and drop it down a tube shaped like 1/4 of a circle, that starts vertical, and curves horizontal, leading to a dead end, while this tube is attatched to wheels.
The act of dropping the ball down the tube vertically, will send the car flying in the horiztonal direction once the ball reaches the dead end.
However, there are some things to keep in mind here.
option 1)
If you do not block the wheels to prevent the car from rolling backwards, the act of dropping the ball down the tube will send the car initially traveling backwards untill the mass reaches the dead end, which will then carry both in the forward direction, but this change of direction in the car will cause a loss in overall momentum, which means, the car will not go as far.
But if you block the vehicle from initially going the wrong way, it will be sent flying into the forward motion with practically zero friction involved.
What kind of materials will you need? A smooth rolling trolley, (wheels and body, like a nicely rolling toy car) to attatched the curved tube to. You could curve cardboard, or some type of material to act as the "ramp" or tube for the ball to travel down. At the end of the ramp, a stiff material to stop the ball. You want to set it up so that the 1kg mass (ball, or cylender for that matter) does not slow down on this path. So, smooth, hard materials would be good, like that stuff art paper used for portfolios and what not.
Option 2)
Or you could even, just throw away the ramp idea, and attach the mass to a string, and rig it up on the car like a swingset. Again, you'd need to block the car from rolling backwards, but you could drop the 1km from 10cm, and cause it to swing into a stopper on the car which would carry the momentum forward. The stopper would need to be something soft to prevent bouncing, like playdoh or, cloth.
However, this will not likely allow the car to travel as far as weight and pulley system. The mass of the car will affect how much acceleration the 1kg mass falling object will deliver to the car. Since the pulley system does not accelerate the car as quickly, the force can be acted out over a larger distance.
If the car and the mass each weigh 1kg, when the two masses join, to travel down the track, the momentum of the swinging/falling mass will be split with the mass of the car for a velocity = to 1/2 of the velocity of the mass before it hit the car.
Where V is velocity
p is momentum
m is mass
Say the 1kg mass(m) is moving at 1m/s (v)when it crashes into the car stopper.
Find momentum of the moving mass first:
*(1))
The velocity of the 1kg car and mass after the crash together is
