Hmmmm
I see this discussion which was started by someone asking "what time is it", so to speak, has degraded into a discussion about the inaccuracies of atomic clocks in as much as Einstein has "proven" that time can go backwards.
One needs no collisions with brick walls or any other extrapolations of Newtonian physics to understand what makes a piano action work, and the best way to work this clever piece of machinery.
As I've noted before, the key travels downward about 3/8ths of an inch or so, and ONLY the first 1/4 of an inch moves the hammer. The last 8th is dead space, after which the key hits the key bed.
So the best way to play as a standard is with the finger on the key, pull the key down quickly and briefly so that the sound occurs, but your finger does not hit cause the key to hit the key bed hard, but to touch it and rebound naturally from the energy of the key bringing the at rest-finger with it, ready to play again.
For clarity's sake, imagine that the key mechanism was a huge model whereby we're talking about a travel distance of 3 feet instead of 3/8ths of an inch.
Why, after pushing the enormous key down 2 feet at which point it has pushed the jack past the hammer knuckle and sent the hammer flying upward into a long large string, would you continue to push the key down with effort to collide hard against the key bed, both doing nothing to effect sound, and incrementally injuring yourself?
Anyone who can look at a key mechanism, think logically, get past their bias, etc., can prove this to one's self.
Again, this has been proven to a scientific certainty by real "piano scientists" many years ago, as well anecdotal evidence from many professional pianists. (Ortmann and Schultz, scientists)
Why would anyone doubt that the faster you pull down the key, the faster the hammer will hit the string and the louder the resulting sound?