Final answer:
The spilling of the milkshake when a car brakes is a result of Newton's first law of inertia, and is best understood by analyzing the forces at play and representing them in a free-body diagram, employing Newton's second and third laws.
Step-by-step explanation:
The scenario presented involves a student experiencing the effects of Newton's laws of motion when their milkshake spills forward as a result of their mom stepping on the brakes. The initial conditions include the car moving at a constant speed with the milkshake at rest in the student's hand. As per Newton's first law, also known as the law of inertia, the milkshake is initially in motion along with the car and tends to continue in this state unless acted upon by an external force. When the brakes are applied, the car experiences a decelerating force which changes the velocity of the car but not the milkshake which results in the milkshake spilling.
To fully understand this, one must draw a free-body diagram representing the forces acting on the milkshake: gravitational force pulling it downward, the normal force from the hand supporting it, and no forward force as the brakes are applied, resulting in the milkshake continuing its motion forward. Newton's second law can be invoked to relate the forces the car exerts on the road to the deceleration it experiences (F=ma). The milkshake's inertia keeps it in motion even though the car decelerates.
Finally, Newton's third law explains the interaction between the car and the road; as the car exerts a force on the road via the brakes, the road exerts an equal and opposite force on the car, causing it to decelerate. The milkshake, not being attached to the car, doesn't experience this force directly and thus continues its forward motion, which we perceive as spilling.