Changes in energy: The kinetic energy of a moving object can be calculated using the equation:

The idea

Kinetic energy is the energy stored in an object because it is moving. It depends on the object's mass and on its speed, and it is measured in joules (J). To calculate it, use the equation Ek = 0.5 × m × v², where m is mass in kilograms and v is speed in metres per second. For example, a 2 kg ball moving at 3 m/s has kinetic energy 0.5 × 2 × 3² = 9 J. Doubling the speed has a much bigger effect than doubling the mass, because speed is squared in the equation. This links to energy transfers: when a moving object slows down, its kinetic energy decreases and is transferred to other stores, such as the thermal store of the brakes via mechanical work.

What earns the marks

• State that kinetic energy is the energy stored in a moving object and is measured in joules (J).
• Identify the two variables that kinetic energy depends on: mass and speed.
• Recall and apply the equation Ek = 0.5 × m × v² to calculate kinetic energy.
• Use mass in kilograms and speed in metres per second before substituting into the equation.
• Recognise that speed is squared, so kinetic energy changes by the square of the speed for a fixed mass.
• Describe energy transfers involving kinetic energy, for example kinetic energy transferred to thermal energy when brakes are applied.

Common mistakes and how to put them right

• Using grams instead of kilograms.

  Put it right: Convert mass to kg by dividing by 1000 before calculating, because the equation requires SI units.

• Forgetting to square the speed.

  Put it right: Calculate v² first, then multiply by 0.5 and the mass.

• Mixing up kinetic energy with other energy equations.

  Put it right: Check whether the question gives speed (use Ek = 0.5 × m × v²) or height (use gravitational potential energy).

Exam tips

• Write down the equation Ek = 0.5 × m × v², then substitute values with units before doing the arithmetic, so method marks are visible.
• Check the unit of every value given; convert g to kg and km/h to m/s if needed.
• When a question asks for a comparison, calculate both kinetic energies and state the ratio or factor clearly.