Kinetic and gravitational potential energy
Physics · Key Stage 3 · The School
Kinetic energy: the energy of movement
Kinetic energy is the energy something has because it is moving. The formula is KE = ½mv², where m is mass in kilograms and v is speed in metres per second. A 2 kg ball moving at 3 m/s has KE = 0.5 × 2 × 3² = 9 J. Notice the speed is squared. That single detail changes everything about how this energy behaves.
Why speed matters more than mass
Double the mass, and KE doubles too — simple and direct. Double the speed instead, and KE goes up by four times, because 2² is 4, not 2. A car going twice as fast does not need twice the stopping distance. It needs about four times as much, which is exactly why speed limits matter more than they might seem to at first glance.
Gravitational potential energy: the energy of height
Gravitational potential energy is the energy something has because of its height above the ground. The formula is GPE = mgh, where m is mass, g is gravitational field strength (about 10 N/kg on Earth), and h is height in metres. Lift a 5 kg box 2 m up, and GPE = 5 × 10 × 2 = 100 J. Lower it back down, and that same 100 J transfers into kinetic energy as it falls.
A 1 kg ball sits on a shelf 5 m up. Its GPE = 1 × 10 × 5 = 50 J. Drop it. As it falls, GPE steadily converts to KE, and just before it hits the floor, KE = 50 J too, because all the GPE has transferred across (ignoring air resistance). Using KE = ½mv², that means ½ × 1 × v² = 50, so v² = 100, so v = 10 m/s. Height told us the energy. Energy told us the speed. Nothing was measured directly — it was all worked out from one formula feeding into the next.