Definition
- Kinetic energy (KE) is the energy an object has because of its motion. Any object with a mass and a speed has kinetic energy
The KE equation
KE = ½ × m × v²
- where:
- KE = energy in the kinetic store (J)
- m = mass of the object (kg)
- v = speed of the object (m/s)
- The square on v is the most important feature of this equation:
- doubling the speed quadruples the kinetic energy
- tripling the speed gives nine times the kinetic energy
- the same factor of four shows up in braking-distance rules (topic 02): twice as much kinetic energy needs twice the distance to remove
Example — a cyclist plus bike together have a mass of 50 kg and are moving at 8.0 m/s along a flat road. Calculate the kinetic energy of the cyclist-and-bike system.
- KE = ½ × m × v² = ½ × 50 × 8.0² = ½ × 50 × 64 = 1600 J
Example — a car of mass 1100 kg accelerates from 12 m/s to 24 m/s on a flat motorway. Calculate the change in its kinetic energy.
- KE at 24 m/s = ½ × 1100 × 24² = ½ × 1100 × 576 = 316 800 J
- KE at 12 m/s = ½ × 1100 × 12² = ½ × 1100 × 144 = 79 200 J
- ΔKE = 316 800 − 79 200 = 237 600 J
- Doubling the speed (12 → 24 m/s) raises the kinetic energy by a factor of four, exactly as the v² in the equation predicts