How does Newton's first law affect roller coasters?

Hint: Newton's first law is also known as the law of inertia. Inertia is the inability to change the state of rest or of motion. A body will remain in its state of rest or of motion until and unless an external force is applied on it.

Complete answer:
Newton's first law states that; A body will remain in its state of rest or of motion until an external force acts on the body. The body will have inertia of motion or inertia of rest unless an external force is applied on it to change its state of inertia(state or rest).
As per the Law, a body will remain in its state of rest or of motion unless an external force acts on it, in the similar manner roller coaster will not run unless a force is applied to run it and again force of brakes is applied to stop the roller coaster from moving. At rest or at motion for both the cases an external force is applied on the roller coaster.

Note: Newton's Second law states that the rate of change of acceleration is equal to the momentum of the body, such as when the rocket is propelled to be launched to go into the space (acceleration is changed to have momentum) and the Newton's third law states that, every action has an equal and opposite reaction such as while pulling the cart horse pushes the road back in order to get a forward force to pull the cart.