A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Kinetic energy is the energy an object has because it is moving. The formula is KE = ½mv², where m is mass in kilograms and v is speed in meters per second. Because velocity is squared, doubling an object's speed quadruples its kinetic energy. This makes speed far more important than mass in determining kinetic energy. Kinetic energy is measured in joules.
Calculate the kinetic energy of familiar objects (a thrown baseball, a moving car, a running person) and compare. Change the speed in the formula and see how dramatically kinetic energy increases. Discuss why car crash damage is so much worse at highway speeds compared to parking-lot speeds.
You already know from everyday experience that moving objects carry energy — a rolling bowling ball can knock down pins, a moving car can crumple a fender, and a thrown basketball can knock a drink off a table. Physics gives this energy a name: kinetic energy, from the Greek word for motion. The formula that quantifies it is KE = ½mv².
Let us break this formula down. The m is mass in kilograms, and v is speed in meters per second. The ½ is just a constant that comes from the mathematics of how work and energy are related. The most important feature is the v² — velocity is squared. This means that speed has a far greater impact on kinetic energy than mass does.
Here is a concrete example. A 1,000 kg car moving at 10 m/s has KE = ½ × 1,000 × 10² = 50,000 J. Now double the speed to 20 m/s: KE = ½ × 1,000 × 20² = 200,000 J. The speed doubled, but the kinetic energy quadrupled. Triple the speed to 30 m/s and the kinetic energy goes up by a factor of nine, to 450,000 J. This is why speed limits exist and why highway collisions are so much more devastating than low-speed fender benders.
Compare this to momentum (p = mv), where doubling speed simply doubles momentum. The squared relationship in kinetic energy makes it a fundamentally different quantity. Two objects can have the same momentum but very different kinetic energies, or vice versa. Each quantity is useful in different situations — momentum for analyzing collisions, kinetic energy for analyzing energy transfers.
Kinetic energy connects directly to the concept of work. The work-energy theorem states that the net work done on an object equals its change in kinetic energy. If you do 100 J of net work on a ball starting from rest, the ball ends up with 100 J of kinetic energy. This tight relationship between work and kinetic energy is one of the most useful tools in physics, allowing you to solve motion problems through energy methods instead of force-and-acceleration methods.