Changes in energy: kinetic energy, E_k, in joules, J

The idea

Kinetic energy is the energy stored by a moving object. The symbol Eₖ represents kinetic energy, and its unit is the joule (J). One joule is the energy transferred when a force of one newton moves an object one metre. In calculations, kinetic energy is found using Eₖ = ½mv², where m is mass in kilograms and v is speed in metres per second. Because speed is squared, small changes in speed cause large changes in kinetic energy.

For example: A 1000 kg car travelling at 10 m/s has Eₖ = ½ × 1000 × 10² = 50 000 J. Understanding the unit and symbol is essential for correct substitution and for interpreting energy values in contexts such as braking distances and safety design.

What earns the marks

• State that kinetic energy is measured in joules (J).
• Use the symbol Eₖ correctly in equations and calculations.
• Recognise that the joule is the unit of energy and is equivalent to a newton-metre (N m).
• Distinguish kinetic energy from other energy stores such as gravitational potential energy or thermal energy.
• Interpret given kinetic energy values in joules and convert to other units such as kilojoules if needed.

Common mistakes and how to put them right

• Confusing the symbol Eₖ with other energy symbols such as Eₚ or Eₑ.

  Put it right: Learn that Eₖ specifically denotes kinetic energy.

• Writing the unit as 'joules' without the capital J or using 'J' incorrectly.

  Put it right: The correct symbol is J, and it is capitalised.

• Thinking that kinetic energy depends only on mass or only on speed.

  Put it right: It depends on both, and speed is squared.

• Using the wrong unit for mass or speed in calculations, leading to an incorrect unit for energy.

  Put it right: Use kg and m/s to obtain joules.

Exam tips

• Always include the unit J when giving a final answer for energy, unless asked to give it in another unit.
• If a question asks for kinetic energy 'in joules', ensure your calculation uses SI units throughout.
• When comparing kinetic energies, calculate both values and state which is larger and by what factor.
• Remember that the symbol Eₖ is often written as E_k in plain text; in handwritten work, use a clear subscript.