We know that the incoming strike has both mass and velocity, which means that it has kinetic energy, which is the energy an object has due to its motion. Work is when a force is applied to an object that then moves in the direction of the force. Kinetic energy and work are the final pieces of the puzzle that we need. The formula for kinetic energy is KE = ½ mv2. The formula for work is W = Fd. So, if the incoming punch has kinetic energy, then the face needs to do work to dissipate that energy. That gives us the equation W = Favgd = ½ mv2. To stop the incoming strike, the guy rolling with the punch will need to provide an average force over a distance d. You could also think of the average force as the impact force felt by the face (remember that every action has an equal but opposite reaction). The greater the distance is the smaller that average force can be. So, impulse told us that we need to increase the impact time and the energy equations told us that we need to increase the impact distance (to avoid taking damage, that is). Those two conclusions both being true isn’t all that surprising. What is interesting about the energy equation is this: when striking, velocity is a much bigger factor than mass. I can say this because of the squared velocity. Let’s consider a qualitative example.
B = ½ (m/2)(2v)2 = (m/4)(4v2) = mv2 = 2KEA. So, B’s punch has twice the kinetic energy of A’s punch, which means that someone will need twice the distance to “roll with the punch” or they’ll just have to feel twice the average impact force. This explains why Bruce Lee had such devastating strikes despite his small size.