Changes in energy: speed, v, in metres per second, m/s

The idea

Speed, v, is the rate of change of distance with time and is measured in metres per second (m/s). In energy calculations, speed must be in m/s before substitution into the kinetic energy equation E_k = ½mv². For example, a 1000 kg car travelling at 15 m/s has E_k = ½ × 1000 × 15² = 112500 J. If speed is given in km/h, convert to m/s by dividing by 3.6: 72 km/h = 20 m/s. Speed is a scalar quantity, while velocity is a vector. When using E_k = ½mv², the speed is squared, so doubling speed quadruples kinetic energy. Always check that speed is in m/s and mass in kg before calculating energy changes.

What earns the marks

• State that speed is measured in metres per second (m/s) and is a scalar quantity.
• Convert speeds given in km/h to m/s by dividing by 3.6 before substitution.
• Use speed in m/s in the kinetic energy equation E_k = ½mv².
• Recognise that kinetic energy is proportional to the square of speed.
• Check that all quantities are in consistent SI units before calculating energy changes.

Common mistakes and how to put them right

• Using km/h directly in the kinetic energy equation instead of converting to m/s.

  Put it right by dividing by 3.6.

• Forgetting to square the speed when calculating kinetic energy.

  Put it right by applying v² before multiplying by ½m.

• Confusing speed with velocity and treating direction as relevant in kinetic energy calculations.

  Put it right by using speed as a scalar in E_k = ½mv².

Exam tips

• Always write the unit m/s after a speed value in your working to show the correct quantity.
• If a speed is given in km/h, convert to m/s in a separate step before substitution to avoid errors.
• In calculations, show the equation, substitution and answer with unit to gain method marks even if the final answer is wrong.