Suppose you imagined a vertically aligned surface and with respect to this imagined (massless) surface were two objects shooting towards each other. Suppose these objects both had mass [itex]m[/itex], and each their kinetic energies (with respect to each other) would be [itex].5mv^2[/itex]. Suppose they are moving along the same line perpendicular to the surface. [itex]v[/itex] is the sum of the velocities with respect to the surface, call these velocities [itex]a[/itex] and [itex]b[/itex]. Is there any significance to the quantity [itex]m(a+b)^2-ma^2-mb^2[/itex] or [itex]mab[/itex]?? In physics, does the product of two different velocities along the same dimension have any meaning? Does this have anything to do with the left over kinetic energy with respect to the imagined surface?