GCSE · Physics · AQA · Spec 8463

Kinetic energy calculation (Ek = 1/2 m v^2)

A little more speed can mean a lot more energy — because the speed is squared.

Speed has a squared effect

1v = 1 m/s231 JKinetic energy

Stage 1 of 3: v = 1 m/s. Kinetic energy: 1 J. paused

v = 1 m/s · 1/3Scrub the speed. Notice 1 → 2 → 3 becomes 1 → 4 → 9 in Eₖ.

m = 2 kg → Eₖ = 1 J.

Keep mass at 2 kg and change only speed.

Kinetic energy

Eₖ = ½mv²

A moving object has energy in its kinetic store. Mass matters once; speed matters squared.

Eₖ in joules (J), m in kilograms (kg), v in metres per second (m/s).

Predict the effect

Mass stays the same.

If speed doubles, what happens to kinetic energy?

Calculate kinetic energy

Problem

A 1200 kg car travels at 20 m/s. Calculate its kinetic energy.

Kinetic energy in transfers

Braking vehiclevsFalling object

The kinetic store can decrease or increase depending on where energy is transferred.

Focus

Kinetic store

Braking vehicle

Decreases as the vehicle slows

Falling object

Increases as the object speeds up

The insight

Kinetic energy tracks motion, but conservation tells you to ask where the energy came from or went.

Energy movement

Braking vehicle

Energy is transferred from the kinetic store and dissipated to other stores

Falling object

Energy shifts from the gravitational potential store into the kinetic store

Useful question

Braking vehicle

How much did the kinetic store decrease?

Falling object

How much energy shifted into the kinetic store?

Equations you need

Taken directly from the exam-board specification.

Ek = 1/2 m v^2

Ek = kinetic energy (J) · m = mass (kg) · v = speed (m/s)

Learn it — you must recall this in the exam

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

  • A moving object has energy in its kinetic store.
  • Use Eₖ = ½mv² with m in kg and v in m/s.
  • Doubling mass doubles kinetic energy; doubling speed makes it four times as large.
  • Use changes in kinetic energy as part of a complete energy-transfer account.
  • For AQA Physics, Eₖ = ½mv² is classified as recall_and_apply in the specification.

The big picture

A moving object has energy in its kinetic store. Calculate it using Eₖ = ½mv², with energy in joules, mass in kilograms and speed in metres per second. Kinetic energy is directly proportional to mass but proportional to the square of speed, so doubling speed quadruples kinetic energy. In transfer situations, calculate the kinetic-store change and connect it to changes in other stores, such as during braking or falling.

Key points

1The factor ½ is part of the equation.
2Only speed is squared: v².
3Convert mass to kilograms and use speed in metres per second before substituting.
4Kinetic energy is measured in joules.
5During braking the kinetic store decreases; during a fall it can increase as the gravitational store decreases.

Worked example

Problem

A 4.0 kg object has 200 J in its kinetic store. Calculate its speed.

⚠ Watch out

Calculating mv² or ½mv. Both are wrong: the equation needs the factor ½ and the square on the speed.

★ Exam tip

For AQA calculations, write Eₖ = ½mv², convert mass to kg, show v² explicitly and keep the unit J. The specification classifies this equation as recall_and_apply.

🧠

Memory hook

Say it with the rhythm: 'half — mass — speed squared.' The last word is the danger word: squared.

✓

Check yourself

Two identical objects move at 3 m/s and 9 m/s. Without calculating their energies separately, how many times as much kinetic energy does the faster one have?

Flashcards

(14)
When does an object have energy in its kinetic store?
When it is moving.
State the kinetic-energy equation.
Eₖ = ½mv².
What are the units for Eₖ, m and v?
Eₖ in J, m in kg and v in m/s.
What happens to kinetic energy if mass doubles at constant speed?
It doubles.
What happens to kinetic energy if speed doubles at constant mass?
It quadruples.
What happens to kinetic energy if speed triples at constant mass?
It becomes nine times as large.
Find Eₖ for m = 2 kg and v = 5 m/s.
Eₖ = ½ × 2 × 5² = 25 J.
Which part of Eₖ = ½mv² is squared?
Only the speed, v.
What two equation details are most often dropped?
The factor ½ and the square on v.
What happens to a vehicle's kinetic store during braking?
It decreases as energy is transferred to internal stores of the brakes and surroundings.
What can happen to kinetic energy as an object falls?
Its kinetic store can increase as its gravitational store decreases.
A car's kinetic energy changes from 90 kJ to 25 kJ. What is the decrease?
65 kJ.
Why convert grams to kilograms before using the kinetic-energy equation?
The equation requires mass in kilograms to give energy in joules.
How does the AQA specification classify Eₖ = ½mv²?
As recall_and_apply.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learning with Lightbulb is opening soon

You can use this lesson now. Join the waitlist and we'll let you know when the full Lightbulb experience is ready.

Keep me posted

More AQA GCSE Physics topics

See the full AQA Physics curriculum →

How this lesson was checked. This AQA GCSE Physics (specification 8463)lesson was published through Lightbulb Learning's human-designed editorial process — the educational standards, accuracy rules and publication checks it must pass were authored and approved by Philip Halpin. It passed subject-specific assessment, automated educational checks and technical publication verification before going live (publication checks completed 26 August 2026). Published pages are monitored, human spot-checking is ongoing across the lesson library, and anything found wrong is corrected or withdrawn. How our lessons are made and checked. Spotted a mistake? Email hello@lightbulblearning.co and we'll review it.

Helpful guides for parents and students