The first looks at the collision in terms of
force and momentum; the second looks at the collision in terms of energy.
Force (F) is acceleration (a) times mass (m): F = m• a. Momentum (p) is mass
times velocity (v): p = m• v. Since acceleration measures change in velocity over time
(t) (put another way, acceleration is the derivative of velocity with respect to time),
force is the derivative of momentum with respect to time. Equivalently, force times
time equals change in momentum, or impulse (p): p=F• t. This is significant
because momentum is a conserved quantity. It can be neither created nor destroyed,
but is passed from one object (the hand) to another (the board). The reason for this
conservation is Newton’s third law of motion, which states that if an object exerts a
force on another object for a given time, the second object exerts a force equal in
magnitude but opposite in direction (force being a vector quantity) on the first object
for the same amount of time so the second object gains exactly the amount of
momentum the first object loses. Momentum is thus transferred. With p a fixed
quantity, F and t are necessarily inversely proportional. One can deliver a given
amount of momentum by transferring a large force for a short time or by transferring
small amounts of force continuously for a longer time.