It is not dependent on the force of the finger on the key only the velocity.
Fleetfingers, you are right. The velocity depends on the force you apply, because force = mass x acceleration. Something that is important to bear in mind, though, is that the moment you've played the note, no amount of force is going to make a difference. It's important to relax the hand once a note's been played, just applying enough force to hold the key down (if it's a held note) otherwise there is unnecessary tension in the hand and arm which can cause problems. If a student is having trouble doing this it may be helpful for them to think of velocity instead of force in order to be able to do this.
The challenge sounds like the one in the middle: start both fingers at the same time and have them end at the same time, but have one end slow and the other end fast. All within a millisecond. Sounds nuts, right?!