Newton's Second Law
Understand Newton's Second Law 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. Newton's second law links resultant force, mass and acceleration through the equation F = ma.
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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
Newton's second law states that the acceleration of an object is proportional to the resultant force acting on it, and inversely proportional to its mass.
The equation is resultant force = mass × acceleration, F = ma. Force in newtons, mass in kilograms, acceleration in metres per second squared.
The two proportionalities work in opposite directions. Doubling the resultant force doubles the acceleration for the same mass. Doubling the mass halves the acceleration for the same force. This is why a loaded lorry accelerates more slowly than an empty one with the same engine.
Revision notes
The equation
Resultant force = mass × acceleration, F = ma.
Force in newtons, mass in kilograms, acceleration in m/s². Rearranged: a = F ÷ m and m = F ÷ a.
The two proportionalities
Acceleration is proportional to the resultant force: doubling the force doubles the acceleration for a given mass.
Acceleration is inversely proportional to mass: doubling the mass halves the acceleration for a given force. Both relationships are examinable.
Applying it
The force in the equation must be the RESULTANT force, not any single force acting.
If several forces act, find the resultant first by adding and subtracting along the line of action, then substitute that value.
Key points
- Resultant force = mass × acceleration.
- Force is in newtons and mass in kilograms.
- Acceleration is in m/s².
- Acceleration is proportional to resultant force.
- Acceleration is inversely proportional to mass.
- Always use the resultant force in the equation.
Worked examples
Example 1
A resultant force of 600 N acts on a car of mass 1200 kg. Calculate its acceleration. [2 marks]
Model answer
Acceleration = resultant force ÷ mass = 600 ÷ 1200 (1 mark) = 0.5 m/s² (1 mark).
Example 2
Calculate the resultant force needed to accelerate a 70 kg object at 3 m/s². [2 marks]
Model answer
Resultant force = mass × acceleration = 70 × 3 (1 mark) = 210 N (1 mark).
Example 3
Explain why a loaded lorry accelerates more slowly than an empty one with the same driving force. [2 marks]
Model answer
Acceleration is inversely proportional to mass (1 mark), so for the same resultant force a greater mass produces a smaller acceleration (1 mark).
Common mistakes
Using a single force instead of the resultant.
The equation requires the RESULTANT force acting on the object.
Getting the proportionalities the wrong way round.
Acceleration rises with force but falls with mass.
Using grams instead of kilograms.
Mass must be in kilograms.
Confusing weight with resultant force.
Weight is one force acting; the resultant may be different.
Exam tips
- Find the resultant force before substituting.
- State both proportionalities when explaining.
- Use kilograms for mass and m/s² for acceleration.
- Write the equation before rearranging.
Key terms
- Newton's second law
- Resultant force equals mass times acceleration.
- Resultant force
- The single force with the same effect as all forces acting.
- Inversely proportional
- One quantity halving as the other doubles.
- Acceleration
- The rate of change of velocity, in m/s².
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.