GCSE · Physics · AQA · Spec 8463
Newton's Second Law (F = m a)
The bigger the push, the bigger the acceleration — but mass fights back.
What you need to know
- Acceleration is directly proportional to resultant force — double the force, double the acceleration (at constant mass).
- Acceleration is inversely proportional to mass — double the mass, halve the acceleration (at constant force).
- F in F = m a is always the RESULTANT force — the vector sum of all forces acting on the object.
- Higher tier: Inertial mass is defined as the ratio of force to acceleration — it measures how hard it is to change an object's velocity.
The big picture
Newton's Second Law tells us how a resultant force changes an object's motion. A larger resultant force produces a larger acceleration, and a larger mass resists that change more. The relationship is captured in F = m a, where F must always be the resultant force, not just any single force acting. Understanding this law is the key to predicting how any object moves when forces are unbalanced.
TONIGHT'S REVISION
Newton's Second Law (F = m a)
How resultant force and mass together determine an object's acceleration
Forces on an accelerating car
Look at the arrows — the resultant force is the combined effect of ALL four. Which direction does it act, and what does that tell you about the acceleration?
Tap a force to see what it does.
Stop and predict
Commit to an answer before you reveal — this is where real understanding gets tested.
A lorry and a sports car experience the same resultant force. The lorry has 10 times the mass of the sports car. Which statement correctly describes their accelerations?
Newton's Second Law — the causal chain
Reason it through
Why does increasing the resultant force on an object (mass unchanged) cause a greater acceleration?
First link · your turn
What does a resultant force actually do to an object's velocity?
Relationship matrix
Tap any cell to reveal it. Tap a column header to read one property down every item.
Each cell hides a short answer and the reason behind it. Predict before you tap.
AQA PAPER 2 · EXAM PRACTICE
AQA mark scheme — spot the marking points
Read the student answer. The examiner's credited phrases are hidden — reveal them to see which lines score marks.
Question
A student pushes two trolleys, one with a small mass and one with a large mass, using the same resultant force. Explain, using Newton's Second Law, why the trolleys have different accelerations. [3 marks]
Student answer
Newton's Second Law states that acceleration is directly proportional to the resultant force and inversely proportional to mass. Because the resultant force is the same for both trolleys, the trolley with the larger mass will have a smaller acceleration. This is because acceleration equals resultant force divided by mass, so a greater mass produces a smaller acceleration for the same force.
Equations you need
Taken directly from the exam-board specification.
F = resultant force (N) · m = mass (kg) · a = acceleration (m/s^2)
Learn it — you must recall this in the exam
Key points
Worked example
Problem
A car of mass 1200 kg experiences a resultant force of 3600 N forwards. Calculate its acceleration.
Memory hook
Think of pushing a shopping trolley: an empty trolley (small mass) flies forward easily — a full trolley (large mass) barely budges for the same push. Same force, different mass, different acceleration.
★ Exam tip
On AQA Paper 2, if a question gives you multiple forces, calculate the resultant before substituting into F = m a — one mark is specifically awarded for using the resultant force, and using a single listed force instead will lose it.
⚠ Watch out
Using just one force (e.g. the engine force) instead of the RESULTANT force — always subtract opposing forces like friction first, then substitute into F = m a.
Check yourself
If you double the mass of an object but keep the resultant force the same, what happens to the acceleration — and why?
Flashcards
(24)State Newton's Second Law in words.
Write the equation for Newton's Second Law.
What does F represent in F = m a?
What are the units of mass, force and acceleration in F = m a?
If the resultant force on an object is doubled (mass constant), what happens to acceleration?
If the mass of an object is doubled (force constant), what happens to acceleration?
A 5 kg object accelerates at 4 m/s². What is the resultant force?
A resultant force of 30 N acts on a 6 kg object. What is its acceleration?
A resultant force of 50 N produces an acceleration of 2.5 m/s². What is the mass?
What is the resultant force on an object moving at constant velocity?
Why must you use the RESULTANT force in F = m a?
What does RP7 investigate?
In RP7, what happens to acceleration as resultant force increases (mass kept constant)?
In RP7, what happens to acceleration as mass increases (force kept constant)?
Higher tier: Define inertial mass.
Higher tier: Which quantity in F = m a is inertial mass?
Higher tier: An object has a large inertial mass. What does this tell you?
A car engine produces 4000 N forwards; friction produces 1000 N backwards. What is the resultant force?
What graph shape shows that acceleration is directly proportional to resultant force?
What graph shape shows the relationship between acceleration and mass (constant force)?
A 2 kg toy car and a 10 kg go-kart experience the same resultant force. Which accelerates more?
What is the direction of acceleration relative to the resultant force?
In RP7, how is a constant resultant force maintained while mass is varied?
Higher tier: A force of 40 N produces an acceleration of 8 m/s². What is the inertial mass?
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.
Learn Newton's Second Law (F = m a) properly — interactive practice, marked questions and flashcards.
Start this lesson freeMore AQA GCSE Physics topics
- Acceleration (a = Δv/t)
- Current, resistance and potential difference (V = I R)
- Density of materials (ρ = m/V)
- Distance and displacement
- Distance–time graphs
- Efficiency
- Energy stores and systems
- Gravitational potential energy (Ep = m g h)
- Kinetic energy calculation (Ek = 1/2 m v^2)
- Newton's First Law
- Power (P = E/t and P = W/t)
- Resultant forces and resolving forces
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 3 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.