The physics of board breaking Pardon my really rusty school physics knowledge.
I heard martial artists talking about the physics of board breaking and one of the things which they mentioned is formula "F=ma". They were talking that the more mass you have and faster you punch the more force you will apply to board and it will break.
However, there are two issues with that:


*

*There is confusion between acceleration and speed. The formula includes acceleration and they talk about speed.

*You can have an object (something heavy) moving without acceleration (meaning that based on F=ma, the F will be 0) and still breaking the board. 


As a result, I am not sure that the formula mentioned above is directly applicable here (I feel it will come more into play when the hand decelerates and the board accelerates at the moment of the punch, not before the punch).
A couple of things comes to mind:


*

*Moving object (a hand) has kinetic energy which will need to dissipate somewhere when the hand punches the board

*People try to minimize the impact surface while hitting a board. It looks like the governing formula is P = F / A (force applied to a unit area).


It feels like I have most of pieces of the puzzle. However, in the end I can't put all of these together.
I would appreciate it if you help me figure out major governing formulas here.
 A: They could probably do a better job explaining it, but it makes sense that the speed will ultimately affect how the board breaks.
A moving object colliding with a stationary object will transfer some momentum to the stationary object; this momentum is lost from itself.  This causes the moving object to lose speed, which is acceleration.  This acceleration that slows down the moving object is due to the force of the collision.
All other factors equal during the collision, the object with the higher speed will transfer more momentum during the collision, which results in more force acting on the board.  The same applies for mass.
Basically, the higher the relative velocity the object has, the more capacity it has to decelerate compared to the stationary board.  This deceleration is what transfers the force, so a faster impact with the board should provide a greater force, all else equal. 
A: 
I heard martial artists talking about the physics of board breaking
  and one of the things which they mentioned is formula "F=ma". They
  were talking that the more mass you have and faster you punch the more
  force you will apply to board and it will break.

Newton's second law relates the net applied force to an object to the acceleration imparted to the object, for a given mass. Although it is relevant to the extent that the acceleration of the hand/forearm determines the velocity of the hand/forearm upon impact, you are right to think more in terms of the kinetic energy.
Per the work energy theorem, the change in kinetic energy of an object (in this case, the hand/forearm) equals the net work done on or by the object, in this case the work done by the hand/forearm on the board. That, in turn, equals the magnitude of the average force applied to the board times the distance the hand/forearm travels through the thickness of the board. The shorter the distance or time, the greater the force.
Since kinetic energy varies as the square of velocity, the key variable is the speed of the hand/forearm upon impact, that is, the key is to maximize the velocity of the hand/forearm upon impact. 
Hope this helps. 
A: There are several factors involved in breaking a board.
The most simplistic analysis would assume that the board breaks when it is sufficiently bent.  Treating the board as a spring, the amount of bending is directly related to the amount of energy delivered by the martial artist's hand, which in turn depends on the mass of the hand and the hand's speed.
But it's much more complicated than that. The board has inertia, so rate-of-onset (shock) makes a big difference.  If the board is hit with the edge of a hand rather than the palm, orientation of the hand relative to the grain is important.  A board cut with its length across the grain will break much easier than a board cut along the grain.  Thickness of the board makes a huge difference.  How and where the board is supported is important.
In a Taiquando class I took in my early thirties, we had to break a pine board about a foot square and 7/8 inches thick.  It was to be tossed in the air, then struck with the edge of your hand on the way down.  What mattered was speed, aligning the grain correctly, and hitting directly in the middle of the board.  Speed was important because slow impact would not make use of the board's inertia to force it to bend: instead, it would just accelerate the board downward without bending it.
Similar principles apply to breaking rocks.  If you want to break a rock, choose one that is relatively flat and long.  Hold it by one end about and inch above another rock.  Hit it in the middle with the palm of your hand.  The rock will break easily when it hits the rock underneath.
