A car is stopped at a red light. When the light turns green, the car starts

accelerating again. In the process, a cup of coffee sitting in a cup-holder spills

out onto the rear seats. Why does this happen?

This happens because of inertia.

Explanation:

Inertia is the ability of a body to remain in its state of rest or relative movement, while an external force is not acting on it.

It is when a body objects to modifying its state of relative rest or movement, including the speed and direction in which this happens.

When a car accelerates, a cup of coffee sitting in a cup-holder spills out onto the rear seats, because it has left its state of rest due to the acceleration force of the car.

See the explanation below

Explanation:

This happens because the coffee was at rest, at the time when the car accelerates to move forward the container containing the coffee also accelerates in the same direction, the liquid when moving suddenly spills. The same will happen if the car slows down, any sudden movement changes will cause the coffee to spill, understood by sudden movements when it accelerates or slows down.