What physics principles are used in roller coaster and car safety?

Help please. :)|||I think momentum is a big one.





Impulse for safety. How fast can they brake the car without endangering those on the cart.





Also how fast can they safely accelerate people so they don't break their necks. This is also impulse related.





I would also believe potential energy and kinetic energy is a big one. Not as much force is needed in a cart falling down a steep hill. Gravitational forces will do a lot of the work.





Work. How much energy needs to be put into that cart to make it move. The cart should not be made of too heavy material. The heavier it is the harder it is to move and more energy is required to make it move.