Science Buddies: "Ask an Expert"

Please help!! For Physical science class I have to create a 12in+ cart/car that will go down an 8 ft long ramp at a height of either 17,27, or 37 in. The cart thing will then have to go down an 8ft by 4ft runway before turning to the right and almost making some sort of u-turn. I understand the front axle has to pivot but I have no idea where to begin..

You need to break down the requirements in terms of physics principals involved.
1) You are starting with some potential energy based on the 17, 27, or 37 inch height of the ramp. This potential energy will be converted to kinetic energy and that is all the energy you have in order to complete the required course.
2) It is unclear from my reading of your requirements whether your vehicle has to travel 8 feet (8x4 ramp) or 16 feet (8 foot ramp plus another 8 feet staying in an 8x4 foot area). In either case, your vehicle has to go straight for some distance and then turn right sharply. This means you will need some reasonably accurate means of measuring the distance traveled and then applying some steering force. Gears or spooling string/ribbon from a free spool to a driven spool that then pulls on some steering lever after the desired distance has been traveled are typical mechanical solutions for these kinds of problems.
3) Because of Newton's first law of motion, a body in uniform motion will tend to stay uniformly in motion, you are going to need some frictional force between your vehicle and the surface in order to turn. This means you really need to know what the material (floor) you are going to be traveling over in order to choose your wheels appropriately so that you have enough side slip friction to turn and not skid but a low enough rolling friction so that you don't slow down and not travel the distance required.
4) Your vehicle has to stay upright and not tip over in the turn. This means that the length, width, and height of the vehicle, its mass and center of gravity all have to be appropriate for making the turn at the speed it will be going based on the potential to kinetic energy conversion that happens going down the 8 foot long ramp and has to do this at three different speeds.
5) Your vehicle will have to have enough mass and low enough frictional forces so that you can travel the 8 (or 16) feet course and still have enough energy to make a turn at the lowest potential energy trial.
6) You need to control the weight/mass balance between the steering wheel(s) and any fixed wheels so there steered wheel(s) will track and not skid.
A three wheeled vehicle is a lot simpler to design a steering mechanism for than a four wheel vehicle so you might want to think about a tricycle like design.
7) Whatever mechanism you use for measuring the distance has to be strong enough to provide the steering, can't create too much drag or pre-steer and go off course and has to be strong enough to not break in multiple tests.

There a several interesting physics problems to be solved to complete this challenge.