Or, said a bit more in line with physics:
It’s not the Vf=Vi+at that kills you, it’s the F=m(deltaV/deltaT)
It’s a little less pithy, but it makes better sense nonetheless. The first equation describes your free fall. Your final velocity (Vf) is equal to your initial velocity (Vi) plus the acceleration you are undergoing (a) times the amount of time you are falling (t). In a free fall, the acceleration acting on you would be the acceleration due to Earth’s gravity (32.2 ft/s/s or 9.81 m/s/s). Multiplying this acceleration times the duration of the fall gives you a velocity at impact (taking into account your initial velocity).
The second equation describes your splat. The force that you impact the ground with (F) is equal to the change in your momentum (m*deltaV) divided by the amount it time it takes for your carcass to come to a complete stop (deltaT). This equation represents the impulse with which you hit the ground. Impulse explains everything from why an egg won’t break when hitting a pillow to how cats can survive falls from great heights.
So, yes, the saying does lose some of its catchy quality when expressed in the terms of physics, but at least you will be accurate when saying it. Plus, it will make all your nerdy friends giggle.