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The gravitational acceleration decreases with the square of the distance from the center of the earth. If the object were falling in a vacuum, this would be the only force acting on the object. But in the atmosphere, the motion of a falling object is opposed by the air resistance or drag. The drag equation tells us that drag is equal to a coefficient times one half the air density (R) times the velocity (V) squared times a reference area on which the drag coefficient is based.
The motion of a falling object can be described by Newton's second law of motion, Force = mass x acceleration. Do a little algebra and solve for the acceleration of the object in terms of the net external force and the mass of the object (acceleration = Force / mass)...
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