3.4.1.7
Kinetic energy depends on mass and the square of speed
Work, Energy & Power — AQA A-Level Physics
Key Definition
Kinetic energy — The energy an object has due to its motion. E_k = 0.5mv^2.
$$E_k = \frac{1}{2}mv^2$$
- Where:
- $E_k$ = kinetic energy (J)
- $m$ = mass (kg)
- $v$ = speed (m s⁻¹)
- Doubling the speed quadruples the kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. (KE is proportional to \(v^{2}\)).
- Only the speed is squared, not the mass or the 0.5.
- EnergyThe capacity to do work. Measured in joules (J). is a scalar, so 'loss of kinetic energyThe energy an object possesses due to its motion.' should not include a negative sign.
Worked Example
A body travelling at 12 m s^-1 has KE = 1650 J. Its speed increases to 45 m s^-1. Find the new KE.
Show Solution
1
Find the mass from initial KE
$$m = \frac{2 \times KE}{v^2} = \frac{2 \times 1650}{12^2} = \frac{3300}{144} = 22.9 \text{ kg}$$
2
Calculate new KE
$$E_k = \frac{1}{2} \times 22.9 \times 45^2 = \frac{1}{2} \times 22.9 \times 2025 = 23000 \text{ J (2 s.f.)}$$
Answer
$E_k = 23000$ J (23 kJ)