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A wad of paper is dropped from a second-story balcony and falls through still air to the ground. 

The force of air resistance increases as the speed of the object with respect to the air increases. Thus the force of air resistance increases as the object falls from rest.

F_net is the resultant of the gravitational force and the force of air resistance.

The gravitational force acts in the direction of motion, downward, while the air resistance acts in the direction opposed to motion, in this case upward.

The increasing air resistance therefore decreases the magnitude of the net force.  The net force remains downward, but decreases in magnitude as the velocity increases.

The acceleration is originally equal to the acceleration of gravity, but after the initial instant the increasing speed results in an increasing force of air resistance.  The resulting decrease in the magnitude of the net force implies (by Newton's Second Law) a decrease in the magnitude of the acceleration.

The object will keep speeding up, but at a lesser and lesser rate.

If the object speeds up enough (as it will if the fall is far enough) the air resistance will eventually approach the weight of the object, so the net force will approach zero and acceleration will approach zero.

The acceleration is originally that of gravity; as the speed of the falling object increases the acceleration approaches zero.

Additional Notes:

Student misconception:  Air resistance works against gravity, thereby decreasing the rate of acceleration. Since Fnet = m * a, a decrease in acceleration would decrease net force.

Clarification by instructor:  Air resistance works against motion, not against gravity. If the object was rising, air resistance would be downward and would therefore reinforce the effect of gravity.