Newton's three laws are used to describe any motion, including the motion of a car (with a passenger in it) on a roller coaster.
Newton's first law, also known as the law of inertia, states that an object will move with a constant velocity (without change in either speed or direction) unless it is acted on by an unbalanced force. The application of this law can be experienced while riding a roller coaster. When the car slows down (for example, when approaching a peak), the passengers in the car fall forward, because they tend to keep moving with the same velocity. On the other hand, when the car accelerates, the passengers are thrown backward, as they tend to keep moving with the slower speed.
Newton's second law describes how the velocity of an object changes if there is an unbalanced force acting on it. The rate of change of velocity, or acceleration, is proportional to this force and inversely proportional to the object's mass. For a passenger in the roller coaster's car, the acceleration is created by the combination of two forces: the force from the car on the passenger, and the force of gravity. Since the roller coaster's track is curved, the acceleration depends on the car's speed (the greater the speed, the greater the acceleration) and the curvature of the track (the greater the curvature, the greater the acceleration). Since one is able to "feel" the acceleration, the faster ride on the steeper track results in the more intense experience.
Finally, Newton's third law describes the interaction between two objects: if one object exerts a force on another, the second object must exert the equal force—but in the opposite direction—on the first object. This law is often summarized as "every action has an equal and opposite reaction." The passenger pushes on the car, and the car pushes on the passenger with an equal force in the opposite direction. An interesting thing happens when the acceleration of the passenger and the car (which, again, depends on the speed and the radius of the curvature of the track) happens to equal the gravitational acceleration. Then, Newton's second law indicates that the force from the car on the passenger is zero, which means that the force from the passenger on the car is also zero—he or she does not push on the car at all! This phenomenon is known as weightlessness, which also happens during a free fall. Thus, the passenger feels as if he or she were jumping off a great height.