Changes in energy: kinetic energy = 0.5 × mass × speed ²

The idea

This equation lets you calculate kinetic energy in joules when mass is in kilograms and speed is in metres per second. The symbol 0.5 is the same as one half, and speed² means speed multiplied by itself. For example, a 1500 kg car travelling at 20 m/s has kinetic energy 0.5 × 1500 × 20² = 300 000 J, or 300 kJ. Because speed is squared, doubling speed multiplies kinetic energy by four for the same mass. You may also need to rearrange the equation: mass = kinetic energy ÷ (0.5 × speed²), and speed = √(kinetic energy ÷ (0.5 × mass)). Always convert units first, then substitute, then calculate, and give the unit J with your answer.

What earns the marks

• Write the equation as kinetic energy = 0.5 × mass × speed² and identify each quantity with its unit.
• Substitute values into the equation using mass in kg and speed in m/s.
• Calculate speed² before multiplying by 0.5 and the mass, following the order of operations.
• Rearrange the equation to find mass or speed when kinetic energy is known.
• Explain that for a fixed mass, doubling speed makes kinetic energy four times larger because of the squared term.
• Give the final answer in joules, converting kJ to J where necessary.

Common mistakes and how to put them right

• Squaring the whole expression instead of only the speed.

  Put it right: Only the speed value is squared, not the mass or the 0.5.

• Forgetting the 0.5 factor.

  Put it right: The equation includes one half, so omitting it doubles the answer.

• Using inconsistent units such as grams with metres per second.

  Put it right: Convert all values to kg and m/s before substituting.

Exam tips

• Show each step of substitution and calculation so that method marks can be awarded even if the final arithmetic slips.
• Round only at the end of the calculation, and give the unit J with your answer.
• For rearrangement questions, write the rearranged equation before substituting numbers to reduce errors.