Kinetic Energy
Master Kinetic Energy for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. A moving object stores kinetic energy given by ½mv², so doubling the speed makes the kinetic energy four times larger.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
The kinetic energy store of a moving object depends on its mass and its speed. The equation is kinetic energy = 0.5 × mass × speed².
Because the speed is squared, it has a much greater effect than the mass. Doubling the mass doubles the kinetic energy, but doubling the speed multiplies it by four. This is why stopping distances increase so sharply with speed.
Units must be consistent: mass in kilograms, speed in metres per second, and kinetic energy in joules. A mass given in grams must be converted to kilograms first, and forgetting that conversion is the most frequent error.
Revision notes
The equation
Kinetic energy = 0.5 × mass × speed², or Eₖ = ½mv².
Mass is in kilograms, speed in metres per second, and kinetic energy in joules. Both the equation and the units are examinable.
Why speed matters more than mass
The speed is squared, so it has a much greater effect on the kinetic energy than the mass does.
Doubling the mass doubles the kinetic energy. Doubling the speed multiplies it by four. Tripling the speed multiplies it by nine.
Rearranging
To find speed: v = √(2Eₖ ÷ m). To find mass: m = 2Eₖ ÷ v².
Square the speed before multiplying, and remember to take the square root at the end when finding speed. Write the equation before substituting.
Key points
- Kinetic energy = 0.5 × mass × speed².
- Mass is in kilograms.
- Speed is in metres per second.
- Kinetic energy is in joules.
- Doubling the speed multiplies the energy by four.
- Convert grams to kilograms before calculating.
Worked examples
Example 1
Calculate the kinetic energy of a 1200 kg car travelling at 20 m/s. [3 marks]
Model answer
Kinetic energy = 0.5 × mass × speed² = 0.5 × 1200 × 20² (1 mark). 20² = 400, so 0.5 × 1200 × 400 (1 mark) = 240 000 J (1 mark).
Example 2
A car doubles its speed. Explain what happens to its kinetic energy. [2 marks]
Model answer
The kinetic energy becomes four times greater (1 mark), because the speed is squared in the equation, so doubling it multiplies the energy by 2² which is 4 (1 mark).
Example 3
Calculate the kinetic energy of a 500 g ball moving at 6 m/s. [3 marks]
Model answer
Convert the mass: 500 g = 0.5 kg (1 mark). Kinetic energy = 0.5 × 0.5 × 6² = 0.5 × 0.5 × 36 (1 mark) = 9 J (1 mark).
Common mistakes
Forgetting to square the speed.
The speed must be squared before multiplying by the mass and by 0.5.
Using grams instead of kilograms.
Mass must be in kilograms, so divide grams by 1000 first.
Doubling the energy when the speed doubles.
It becomes four times greater, because the speed is squared.
Forgetting the square root when finding speed.
Rearranging gives v² first, so the root is the final step.
Exam tips
- Write the equation before substituting any numbers.
- Square the speed as a separate step.
- Convert mass to kilograms first.
- State joules as the unit for energy.
Key terms
- Kinetic energy
- The energy stored by a moving object.
- Mass
- The amount of matter, measured in kilograms.
- Speed
- How fast an object moves, in metres per second.
- Joule
- The unit of energy.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.