IGCSE Physics / Work and power
Kinetic energy
Edexcel International GCSE Physics (4PH1), chapter 16: Work and power, specification point 4.14. Free lesson.
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Kinetic energy is the energy an object has because it is moving. The equation lets you calculate kinetic energy, mass or speed, and shows why changing speed has a large effect on kinetic energy.
What kinetic energy depends on
A moving object has energy in its kinetic store. Its kinetic energy depends on its mass and speed. The equation is KE = 1/2 × m × v². KE is measured in joules (J), mass in kilograms (kg), and speed in metres per second (m/s). Only the speed is squared, so square v before multiplying by half the mass. The equation is on the equation list. KE means energy in the kinetic store. m is mass and v is speed.
How to calculate kinetic energy
Put the mass and speed into the equation. Work out the squared speed first, then multiply by half the mass. This order helps you avoid squaring the whole expression by mistake.
Why doubling speed quadruples kinetic energy
Speed is squared in the equation, so kinetic energy does not increase in direct proportion to speed. If the speed doubles, the squared speed becomes four times as large because 2² = 4. The graph for a 2 kg ball curves upwards, showing kinetic energy increasing more steeply as speed rises. At 4 m/s, the 2 kg ball has 16 J of kinetic energy. At 8 m/s, it has 64 J, which is four times as much. So doubling the speed makes kinetic energy four times greater.
How to find speed or mass
When you know kinetic energy and mass, rearrange the equation to find v² first. Then take the square root to find speed. When you know kinetic energy and speed, calculate 1/2 × v² and divide the kinetic energy by this value to find mass. For speed, the value you first find is v², not v. For mass, divide KE by 1/2 × v².
Avoid squaring the wrong part
The brackets around 1/2 × m do not belong inside the square. Only v is squared. For a 0.4 kg ball moving at 5 m/s, square 5 to get 25, then multiply by 1/2 and 0.4. This gives 5 J, not 1 J. Correct: KE = 0.5 × 0.4 × 5² = 5 J. Incorrect: (0.5 × 0.4 × 5)² = 1 J.