Kinetic Energy

Kinetic energy (E_k) is the energy an object has due to its translational motion (i.e. because it's moving)
- The faster an object is moving, the greater its kinetic energy
When an object is falling, it is gaining kinetic energy since it is accelerating under gravity
This energy is transferred from the gravitational potential energy it is losing
An object will maintain this kinetic energy unless its speed or mass changes

Kinetic energy can be calculated using the following equation:

$E_{k} = \frac{1}{2} m v^{2}$

Where:
- E_k = kinetic energy (J)
- m = mass (kg)
- v = velocity (m s^–1)

Kinetic energy diagram, downloadable AS & A Level Physics revision notes

Kinetic energy: The energy an object has when it is moving

Another quantity that also depends on mass m and velocity v is momentum
Therefore, kinetic energy can be written in terms of momentum p, using the equation

$E_{k} = \frac{p^{2}}{2 m}$

Where:
- p = momentum (kg m s^–1)

This form is very useful in particle physics, when comparing the momentum and kinetic energy of a particle

Worked example

A body travelling with a speed of 12 m s^–1 has kinetic energy 1650 J. The speed of the body is increased to 45 m s^–1.

Estimate the body's new kinetic energy.

WE - kinetic energy answer image, downloadable AS & A Level Physics revision notes

Examiner Tip

When using the kinetic energy equation, note that only the speed is squared, not the mass or the ½. If a question asks about the ‘loss of kinetic energy’, remember not to include a negative sign since energy is a scalar quantity.

Both variations of the kinetic energy equation are given in your data booklet. You will most likely use $\frac{1}{2} m v^{2}$ in a mechanics question, and $\frac{p^{2}}{2 m}$ in particle physics.

If you are not convinced these are in fact the same equation:

$E_{k} = \frac{p^{2}}{2 m} = \frac{{(m v)}^{2}}{2 m} = \frac{m^{2} v^{2}}{2 m} = \frac{m v^{2}}{2} = \frac{1}{2} m v^{2}$

Kinetic Energy (HL IB Physics)

Revision Note

Kinetic Energy

Worked example

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Author: Ashika