I recently began browsing the 5e PHB when I noticed that there was no distance per round when falling under the Falling category. Is there a set fall speed and if so, what is it?
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The rules have no explicit guidance on falling kinematics. Mostly.
Free-falling motion isn't tackled in the rules. Back to that in a moment.
Feather Fall allows one to fall at 60 ft. per round (6 sec.), or at a speed of 10 fps without suffering damage. Free-fall, which is injurious, should be faster than that. A little high-school physics will tell us that a body falling freely (assuming g=32 ft/s2) for 10 ft. will attain a final speed of ~25 fps. So this all makes sense: 10fps=no damage, 25fps=1d6 damage.
To me this means it's not inherently unreasonable to use the simple classical physics in this situation: assuming acceleration due to gravity similar to that experienced at sea level on Earth and ignoring air resistance at low speeds:
starting from rest: d1 round=576 ft
starting from rest: dn rounds=576 x n2 ft
For those who really want a refresher on simple kinematics, assuming uniform acceleration and starting velocities of zero:
In bad (non-SI) units the acceleration due to gravity is approximately 32 feet per second2.