Kinetic Energy

Extended tier only

Energy in an object's kinetic store is defined as:

The amount of energy an object has as a result of its mass and speed

This means that any object in motion has energy in its kinetic energy store
- If an object speeds up, energy is transferred to its kinetic store
- If an object slows down, energy is transferred away from its kinetic store

Kinetic energy of a moving object

A moving car has energy in its kinetic store

Kinetic energy equation

The amount of energy in an object's kinetic store can be calculated using the equation:

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

Where:
- $E_{k}$ = kinetic energy, measured in joules (J)
- $m$ = mass of the object, measured in kilograms (kg)
- $v$ = speed of the object, measured in metres per second (m/s)
The kinetic energy equation demonstrates that if the mass of an object is doubled for a given speed, then its kinetic energy will double
- This is because kinetic energy is directly proportional to mass
- $E_{k} \propto m$
If the speed of the object is doubled for a given mass, it will have four times the kinetic energy
- This is because kinetic energy is directly proportional to velocity squared
- $E_{k} \propto v^{2}$

Worked example

Calculate the kinetic energy stored in a vehicle of mass 1200 kg moving at a speed of 27 m/s.

Answer:

Step 1: List the known quantities

Mass of the vehicle, $m = 1200 kg$
Speed of the vehicle, $v = 27 m / s$

Step 2: Write down the equation for kinetic energy

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

Step 3: Calculate the kinetic energy

$E_{k} = \frac{1}{2} \times 1200 \times {(27)}^{2}$

$E_{k} = 437 400 J$

Step 4: Round the final answer to 2 significant figures

$E_{k} = 440 000 J (2 s . f .)$

Examiner Tip

When performing calculations using the kinetic energy equation, always double-check that you have squared the speed. Forgetting to do this is the most common mistake that students make.

You will most likely need to rearrange the kinetic energy equation in your IGCSE Co-ordinated Sciences exam. The kinetic energy equation is one of the more difficult rearrangements at IGCSE, so make sure you are comfortable doing it before your exam!

Kinetic Energy (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Revision Note

Kinetic energy

Kinetic energy of a moving object

Kinetic energy equation

Worked example

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Author: Leander