In Newton's theory of mechanics, given two bodies, each with mass m, starting at the origin and moving along the x -axis in opposite directions, one with speed v 1 and the other with speed v 2 the total kinetic energy of the system (as calculated from an observer at the origin) is ⁠ 1 / 2 ⁠ m (v 1 + v 2) and remains the same if the velocities are interchanged. The total kinetic energy is preserved under a reflection in the y -axis.