But is it really the sudden stop?

[starslayer]

If you are dissapating all of the energy instantly across the body, the energy must still be dissapated.

I suggest plugging it into the terminal balistics model that Douglas wrote up ( http://www.sjgames.com/pyramid/sample.html?id=2794 ). Use the largest cross sectional area

Chances are that in most applications the damage is so close to zero as to round down to zero; but if you start getting into some stupid speeds above terminal velocity on earth it may become relevant.

TL/DR // DDC (Don't Do Calculus): On earth, for objects not going above terminal velocity it does zero damage (for ease of calculation terminal velicoty is 50 yards/second), if the object is going above terminal velocity it does 1 damage, and 1 more damage for every mutiple above (2 damage at 100 m/s, 4 damage at 200, 60,000 damage to be instantly decelerated from the speed of light to full stop)

[whswhs]

Originally Posted by starslayer

If you are dissapating all of the energy instantly across the body, the energy must still be dissapated.

I suggest plugging it into the terminal balistics model that Douglas wrote up ( http://www.sjgames.com/pyramid/sample.html?id=2794 ). Use the largest cross sectional area

Cross sectional area is relevant if the force is being applied to the surface area of the falling body's underside. But if it's being applied throughout the interior of the body the cross sectional area doesn't come in.