Translational Kinetic Energy

Kinetic energy is the energy an object has because it is moving: K = ½mv². The speed enters squared, so the energy is much more sensitive to speed than to mass. Double the speed and the kinetic energy does not double, it quadruples; triple the speed and it grows ninefold. That one feature, the square on the v, drives most of what is surprising about energy.

Two big habits and one quiet one. The loud mistakes: treating kinetic energy as proportional to speed rather than to its square, so a car at 20 m/s looks like it carries twice the energy of one at 10 m/s when it actually carries four times as much; and forgetting that kinetic energy depends on the frame, since the speed in K = ½mv² is measured against a chosen inertial frame, so a passenger sitting still in a moving train has zero kinetic energy in the train frame and a large one in the ground frame. The quiet one is giving energy a direction or a sign at all — kinetic energy is a non-negative scalar, and the vector that carries direction is the momentum p = mv.