Kinetic energy is the energy that an object or system has because of its motion: moving objects have the ability to exert force over a distance when they collide with other objects. The kinetic energy of a moving object is equal to half its mass times the square of its speed:
kinetic energy = ½ mass × speed^{2}

Kinetic energy is similar to momentum in some respects. Obviously, anything with momentum has kinetic energy, and *vice versa*. Moreover, momentum and energy both are conserved quantities—quantities that don’t change in a closed system. However, there are some important differences between momentum and kinetic energy:

- Momentum is a vector quantity (it has direction); energy is a scalar quantity (it doesn’t have direction).
- Unlike energy, momentum is
*not*directly related to an object’s ability to exert force when it collides with other objects.

This second point may seem counterintuitive. You might think that the greater an object’s momentum, the greater its ability to push things. In other words, you might think that something with a lot of momentum (a moving freight train, for instance) will be able to exert more force over any given distance than something with little momentum. But that’s not always true! Notice that the “speed” term is squared in the equation for kinetic energy, but not in the equation for momentum:
kinetic energy = ½ mass × speed^{2}
momentum = mass × velocity
Therefore, increasing the speed makes a bigger difference to an object’s energy than to its momentum. For this reason, it’s possible for something with little momentum to have much greater kinetic energy (i.e. much greater ability to do work) than something with a lot of momentum.

Suppose a 500 kg boulder is moving at 1 m/s, and a 0.02 kg pebble is moving at 500 m/s. The boulder has fifty times more momentum than the pebble:
momentum of boulder = 500 kg × 1 m/s = 500 kg m/s
momentum of pebble = 0.02 kg × 500 m/s = 10 kg m/s
Yet the pebble has ten times more kinetic energy than the boulder:
kinetic energy of boulder = ½ × 500 kg × (1 m/s)^{2} = 250 J
kinetic energy of pebble = ½ × .02 kg × (500 m/s)^{2} = 2,500 J
Even though the massive boulder has fifty times more momentum than the pebble, the tiny (but faster) pebble has ten times greater ability to push things. The boulder can push with 250 newtons of force for 1 meter, but the pebble can exert 2,500 newtons for that same distance! Or, the pebble could exert 25 newtons for 100 meters, but the boulder can only push that hard for 10 meters. Wimpy boulder.

Think about a bullet fired from a rifle. According to the law of conservation of momentum, the total momentum of the system must stay the same before and after the gun is fired. Since the momentum was zero initially (nothing was moving), the momentum of the speeding bullet must be equal in magnitude and opposite in direction to the momentum of the recoiling rifle. The bullet and the gun have the same amount of momentum, in opposite directions. So why is the bullet able to penetrate a target, while the rifle doesn’t penetrate the shoulder of the marksman? The reason is that the bullet has much greater kinetic energy—it can exert much greater force for any given distance. That’s why the relatively light but fast-moving bullet is able to penetrate into a target, while the recoiling rifle doesn’t exert nearly as much force on the marksman’s shoulder (fortunately).