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?

Car (1000 kg)Engine force (F_engine)Friction (F_friction)Weight (W)Normal contact force (N)

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

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Reason it through

Why does increasing the resultant force on an object (mass unchanged) cause a greater acceleration?

Link 1 of 3

First link · your turn

What does a resultant force actually do to an object's velocity?

2
Locked — reveal the link above first
3
Locked — reveal the link above first
Higher

Relationship matrix

Tap any cell to reveal it. Tap a column header to read one property down every item.

Acceleration from 4000 N resultant forceInertial mass (Higher tier: F ÷ a)Resistance to velocity change
Sports carmass = 800 kg
Lorrymass = 8000 kg

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.

Method marks0/3

Equations you need

Taken directly from the exam-board specification.

F = m a

F = resultant force (N) · m = mass (kg) · a = acceleration (m/s^2)

Learn it — you must recall this in the exam

Key points

1F = m a — resultant force equals mass times acceleration.
2Bigger resultant force → bigger acceleration (mass constant).
3Bigger mass → smaller acceleration (force constant).
4The resultant force is the combined effect of all forces acting — never just one of them.
5Higher tier: Inertial mass = force ÷ acceleration; a large inertial mass means the object strongly resists changes to its velocity.

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.
The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.
Write the equation for Newton's Second Law.
F = m a
What does F represent in F = m a?
The resultant force — the vector sum of all forces acting on the object, measured in newtons (N).
What are the units of mass, force and acceleration in F = m a?
Mass: kg; Force: N; Acceleration: m/s².
If the resultant force on an object is doubled (mass constant), what happens to acceleration?
Acceleration doubles — acceleration is directly proportional to resultant force.
If the mass of an object is doubled (force constant), what happens to acceleration?
Acceleration halves — acceleration is inversely proportional to mass.
A 5 kg object accelerates at 4 m/s². What is the resultant force?
F = 5 × 4 = 20 N.
A resultant force of 30 N acts on a 6 kg object. What is its acceleration?
a = 30 ÷ 6 = 5 m/s².
A resultant force of 50 N produces an acceleration of 2.5 m/s². What is the mass?
m = 50 ÷ 2.5 = 20 kg.
What is the resultant force on an object moving at constant velocity?
Zero — no acceleration means no resultant force.
Why must you use the RESULTANT force in F = m a?
Because acceleration is caused by the overall net effect of all forces combined, not by any single force in isolation.
What does RP7 investigate?
How acceleration depends on resultant force (at constant mass) and on mass (at constant force).
In RP7, what happens to acceleration as resultant force increases (mass kept constant)?
Acceleration increases proportionally — the graph of acceleration against resultant force is a straight line through the origin.
In RP7, what happens to acceleration as mass increases (force kept constant)?
Acceleration decreases — the graph of acceleration against mass is a downward curve (inverse relationship).
Higher tier: Define inertial mass.
Higher tier: Inertial mass is a measure of how difficult it is to change an object's velocity; it is defined as the ratio of force to acceleration.
Higher tier: Which quantity in F = m a is inertial mass?
Higher tier: m — rearranging gives m = F ÷ a, which is exactly the definition of inertial mass.
Higher tier: An object has a large inertial mass. What does this tell you?
Higher tier: A large inertial mass means a large force is needed to produce even a small acceleration — the object strongly resists changes to its velocity.
A car engine produces 4000 N forwards; friction produces 1000 N backwards. What is the resultant force?
Resultant force = 4000 − 1000 = 3000 N forwards.
What graph shape shows that acceleration is directly proportional to resultant force?
A straight line through the origin on an acceleration–force graph.
What graph shape shows the relationship between acceleration and mass (constant force)?
A downward curve (inverse/reciprocal curve) on an acceleration–mass graph.
A 2 kg toy car and a 10 kg go-kart experience the same resultant force. Which accelerates more?
The toy car — it has less mass, so the same force produces a greater acceleration.
What is the direction of acceleration relative to the resultant force?
Acceleration acts in the same direction as the resultant force.
In RP7, how is a constant resultant force maintained while mass is varied?
A fixed hanging mass provides the force via a pulley; the trolley mass is changed between runs.
Higher tier: A force of 40 N produces an acceleration of 8 m/s². What is the inertial mass?
Higher tier: Inertial mass = F ÷ a = 40 ÷ 8 = 5 kg.

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