kinetic energy
A moving object can do things a still one cannot: a swung hammer drives a nail, a rolling bowling ball knocks down pins, wind spins a turbine. Kinetic energy is the energy an object has because it is moving — its stored ability to do work by virtue of its motion. The faster it goes and the more mass it has, the more kinetic energy it carries.
The exact recipe is K = 1/2 m v^2 — one half the mass times the speed squared. The v^2 is the surprising part: doubling the speed does not double the kinetic energy, it quadruples it, because 2 squared is 4. A car at 60 km/h carries four times the kinetic energy it had at 30 km/h. Kinetic energy is a scalar (it has size but no direction), it is measured in joules (J), and it is never negative — the smallest it can be is zero, when the object is at rest.
That v^2 has life-and-death consequences. Because kinetic energy grows with the square of speed, and stopping means getting rid of all that energy, a car going twice as fast needs roughly four times the braking distance and crashes with four times the energy. Kinetic energy is also the bridge between force and motion: the work-energy theorem says the net work done on an object equals the change in its kinetic energy.
A 1000 kg car moving at 20 m/s has kinetic energy K = 1/2 x 1000 x 20^2 = 1/2 x 1000 x 400 = 200,000 J. Speed it up to 40 m/s and K = 1/2 x 1000 x 1600 = 800,000 J — four times as much, from doubling the speed.
Double the speed, quadruple the kinetic energy — the hidden reason speed matters so much in a crash.
Kinetic energy depends on speed squared, not speed, so it is always positive and never has a direction — unlike momentum (p = m v), which does point a way. Two identical cars heading toward each other carry opposite momenta but the same kinetic energy.