Final answer:
Newton's first law, also known as the law of inertia, explains why the coffee cup continues to move forward and spills when the car suddenly stops; the cup tends to maintain its state of motion (constant velocity) until acted upon by an external force.
Step-by-step explanation:
The phenomenon described in the question is an illustration of Newton's first law of motion, often referred to as the law of inertia. According to this law, an object will continue to be at rest or move at a constant velocity in a straight line unless acted upon by an external force. In the case of John driving his car at a constant velocity and suddenly applying the brakes, the car experiences a deceleration due to the force of the brakes. However, the coffee cup, which was moving at the same velocity as the car, continued to move forward due to inertia until it spilled because there was no external force applied directly to it. This demonstrates that the coffee cup's motion remains unchanged until an external force—like the dashboard coming into contact with it—causes a change.