Impulse and force in a karate chop, can we maximize force minimizing the time of impact? I have heard that we can maximize the force by minimizing the time of impact in a punch.
If that is true, the paradox is if we increase the time of contact with the same amount of force still we increase the impulse. Which is more reelevant force or impulse?
 A: Just to clarify, impulse is force times time.  Which one matters depends on what you are trying to achieve.
If you want to propell a ball thru the air, then it's the impulse that matters.  Note that a ball whacked for a short time by a bat at high force can go further than you can throw by applying lower force and much longer time.
If you are trying to break a board with a karate chop, it is largely the force that matters.  Once the board has cracked, which happens quickly due to the shock wave, additional applied force is of little benefit.
A: impulse is what you feel and force is what you receive. A whip feels more than a punch. If punch is delivered with the same speed as whip and then the hand is withdrawn back quickly then there is no doubt punch will be more effective.. but withdrawing the hand instantaneously is difficult practically, by minimizing the time of contact, practically speaking your punch will not be in contact with the object.. while a tip of a whip is light, fast and flexible and with the least time it can deliver all the force.. in a karate chop we use blade or knife hand, not a punch.. Comparatively a karate chop(knife hand has less area) than a punch.. so it can deliver the total force completely in less amount of time than the punch..  
