Kinetic and Potential Energy Calculations — AQA GCSE Physics
Moving and raised objects store energy that can be calculated and transferred between stores.
Kinetic energy
The kinetic energy of a moving object depends on its mass and the square of its speed: $$E_k = \tfrac{1}{2} m v^2$$
- mass in kg, speed in m/s, energy in joules.
Because speed is squared, doubling the speed gives four times the kinetic energy.
Gravitational potential energy
The gravitational potential energy of a raised object: $$E_p = m , g , h$$
- m = mass (kg), g ≈ 9.8 N/kg, h = height (m).
Elastic potential energy
The energy stored in a stretched spring (within the limit of proportionality): $$E_e = \tfrac{1}{2} k e^2$$
- k = spring constant (N/m), e = extension (m).
Energy transfers
When an object falls, gravitational potential energy is transferred to kinetic energy. Ignoring air resistance, the energy is conserved, so: $$mgh = \tfrac{1}{2}mv^2$$ This can be used to find the speed of a falling object.
Worked example
A 2 kg ball moving at 3 m/s: Eₖ = ½ × 2 × 3² = ½ × 2 × 9 = 9 J.
Exam tips
- Learn Eₖ = ½mv², Eₚ = mgh and Eₑ = ½ke².
- Kinetic energy depends on speed² — doubling speed quadruples Eₖ.
- A falling object transfers Eₚ → Eₖ (use mgh = ½mv²).
- Watch units (kg, m/s, m) and show working.