Making roller coaster need help.

Alright, as my title tells you I am making a roller coaster. I am doing it for a physics class project and I decided on momentum cause my teacher wants something creative :( (I got like 9-10 weeks to do this, so I figure I might as well do this)

Well I need to keep the cart (or camera) on a predefine path to give it the first to stimulate the roller coaster ride. I am not want something advance or just a simple code to do so. I got some ideas oh how and make certain points and use transform.MoveTo but I don't think it would work right. So any idea and with a way to change the speed when I need to?