Why is acceleration negative in a free fall?

Your choice of coordinate systems determines whether acceleration is positive or negative. For example, if you define position zero as the ground and all points above it as having positive altitudes, then the acceleration due to gravity will point in the negative direction.

There is an interesting fact to consider: gravity still acts in a downward direction, but when you are standing, the floor beneath you exerts a force that resists your free fall. This force is up (in the positive direction) and keeps you from falling into the center of the earth. Additionally, the upward force from the floor is equal to and opposite to your weight. Weight is defined as mass times the force of gravity.

Acceleration is negative in a free fall because it acts in the opposite direction to the conventionally chosen positive direction. When an object falls, it accelerates due to gravity pulling it downwards. Since the downward direction is usually chosen as negative in physics, the acceleration of the falling object is assigned a negative value.