There is a geometric way one can show the relation between kinetic energy and momentum which is a mathematical curiosity in my opinion. Let the mass of an object be equal to 2 PI. Then: P = 2 pi v KE = 1/2 (2 pi ) v sq or KE = pi v sq Hence, graphically, if we set v = r, where r is the radius of a circle, we have a circle whose circumference is momentum, 2 pi v, and whose area is the kinetic energy, pi v sq. Thus, for the case where the mass is 2 pi, we see the kinetic energy is geometrically bounded by the momentum of the object. Interesting. Wonder what would happen to this circle at relativistic velocities?