Changes in energy: Eₖ = ½mv²

The idea

This equation calculates the kinetic energy stored by an object due to its motion. Eₖ is kinetic energy in joules (J), m is mass in kilograms (kg), and v is speed in metres per second (m/s). The speed is squared, so doubling speed quadruples kinetic energy. For example, a 2 kg ball moving at 3 m/s has Eₖ = ½ × 2 × 3² = 9 J. When using the equation, first identify the mass and speed, convert grams to kilograms and km/h to m/s if needed, square the speed, multiply by mass, then halve. Rearranging allows calculation of mass or speed from kinetic energy. This equation applies to any moving object in GCSE physics and is central to analysing energy transfers in collisions, braking, and sports.

What earns the marks

• State that Eₖ is kinetic energy measured in joules (J).
• Identify m as mass in kilograms (kg) and v as speed in metres per second (m/s).
• Substitute numerical values correctly into Eₖ = ½mv², including squaring the speed before multiplying by mass and ½.
• Convert units where necessary, for example grams to kilograms or km/h to m/s, before substitution.
• Rearrange the equation to make m or v the subject when required.
• Interpret the result as the kinetic energy of the object in joules.

Common mistakes and how to put them right

• Forgetting to square the speed.

  Put it right: Square the speed value before multiplying by mass and ½.

• Using mass in grams instead of kilograms.

  Put it right: Convert grams to kilograms by dividing by 1000.

• Multiplying by ½ after squaring only the mass or speed incorrectly.

  Put it right: Apply the order of operations correctly, square v first, then multiply by m, then by ½.

• Using speed in km/h without converting to m/s.

  Put it right: Convert km/h to m/s by dividing by 3.6.

Exam tips

• Write down the equation, substitute values clearly, and show each step of working so method marks can be awarded even if the final answer is wrong.
• Check that the final unit is joules (J); if not, re-check unit conversions.
• When rearranging, use inverse operations carefully and check by substituting back into the original equation.
• For higher-tier questions, you may need to combine this equation with others, such as gravitational potential energy or work done, so keep track of energy transfers.