Acceleration and Newton's LawsAQA GCSE Physics: Revision notes

Section 1

What is acceleration and how do you calculate it?

Acceleration is the rate of change of velocity. It describes how quickly an object's velocity changes over time.

The equation for acceleration is:

a = Δv / t

Where:

a = acceleration (m/s²)
Δv = change in velocity (m/s) = final velocity – initial velocity (v – u)
t = time taken (s)

Key points:

Acceleration can be positive (speeding up) or negative (slowing down, also called deceleration)
If acceleration is zero, the object is moving at constant velocity or at rest
Acceleration is a vector quantity, so direction matters

Key termsaccelerationvelocitydecelerationvector quantity

Example

A car increases its velocity from 10 m/s to 25 m/s in 5 seconds. Calculate acceleration: a = (25 – 10) / 5 = 15 / 5 = 3 m/s². The car accelerates at 3 m/s².

Exam tip

Always show the equation clearly and substitute numbers with units. The examiner marks method as much as the final answer.

Section 2

What are the kinematic equations for constant acceleration? (HT)

For objects moving with constant acceleration, two additional equations are essential:

v² = u² + 2as

Where:

v = final velocity (m/s)
u = initial velocity (m/s)
a = acceleration (m/s²)
s = displacement (m)

s = ut + ½at²

Where:

s = displacement (m)
u = initial velocity (m/s)
t = time (s)
a = acceleration (m/s²)

When to use each equation:

Use v² = u² + 2as when you do NOT know time
Use s = ut + ½at² when you know time and need displacement
Use a = Δv/t when you know the change in velocity and time

Key termskinematic equationsdisplacementconstant acceleration

Example

A ball rolls down a ramp with acceleration 2 m/s² for 4 seconds, starting from rest. Find displacement: s = (0)(4) + ½(2)(4)² = 0 + ½(2)(16) = 16 m.

Common mistake

Students often forget the ½ in the equation s = ut + ½at², or use the wrong equation entirely. Always identify which variables you know before choosing an equation.

Section 3

What is Newton's First Law and what does it mean?

Newton's First Law of Motion states:

An object remains at rest or continues to move at constant velocity unless acted upon by a resultant (net) force.

Key implications:

A stationary object stays stationary unless a force pushes or pulls it
A moving object continues moving at the same speed and direction unless a force changes this
This only applies when the resultant force is zero
If forces are balanced (equal and opposite), the object behaves as though no force is acting

Real-world examples:

A book lying on a table stays put (no resultant force)
A spacecraft moving through space at constant velocity continues indefinitely with no engine (no friction in space)
A cyclist coasting at constant speed on a flat road experiences balanced forces (push of pedals balanced by air resistance and friction)

Key termsNewton's First Lawresultant forceequilibrium

Think of it like this

Think of a hockey puck on smooth ice: it slides forever at constant speed unless you hit it. That's because friction (the resultant force) is nearly zero. On regular ground, friction slows it down—a resultant force acts.

Exam tip

Examiners expect you to explain that the object moves at constant velocity, not just 'keeps moving'. Emphasise that acceleration only happens when there is a resultant force.

Section 4

What is Newton's Second Law and how do you use F = ma?

Newton's Second Law of Motion states:

The acceleration of an object is directly proportional to the resultant force and inversely proportional to the mass.

This is expressed as the equation:

F = ma

Where:

F = resultant force (N, Newtons)
m = mass (kg)
a = acceleration (m/s²)

Key points:

The larger the resultant force, the greater the acceleration
The larger the mass, the smaller the acceleration (for the same force)
This law links forces, mass, and acceleration
The resultant force is the net force after all forces are combined

Inertia and inertial mass (HT):

Inertia is the tendency of an object to resist changes in its motion
Inertial mass is a measure of how much an object resists acceleration; it is defined by the equation m = F/a
An object with greater inertial mass requires a larger force to produce the same acceleration
Inertial mass is different from gravitational mass, though they are equal in value

Key termsNewton's Second LawF = mainertiainertial massresultant force

Example

A 1500 kg car experiences a resultant force of 3000 N. Calculate acceleration: F = ma, so 3000 = 1500 × a, therefore a = 3000 / 1500 = 2 m/s².

Exam tip

Always identify the resultant force in the question. If multiple forces are mentioned, you must resolve them first (add or subtract depending on direction).

Common mistake

Students sometimes forget to use the resultant force. If a 10 N push and a 3 N friction force act in opposite directions, use 7 N (the resultant), not 10 N.

Section 5

What is Newton's Third Law and what are action-reaction pairs?

Newton's Third Law of Motion states:

For every action, there is an equal and opposite reaction force. Forces always act in pairs.

Key characteristics of action-reaction pairs:

The two forces are equal in magnitude (size)
The two forces are opposite in direction
The two forces act on different objects
The two forces are of the same type (both contact or both gravitational, etc.)
They act simultaneously

Common examples:

Situation	Action	Reaction
Person pushing a wall	Person exerts force on wall	Wall exerts force on person
Book resting on table	Earth pulls book downward (weight)	Book pulls Earth upward
Swimming	Swimmer pushes water backwards	Water pushes swimmer forwards
Car engine	Car pushes exhaust gases backwards	Exhaust gases push car forwards
Rocket in space	Rocket pushes fuel downwards	Fuel pushes rocket upwards

Important note:

Action-reaction pairs do NOT cancel out because they act on different objects
You cannot add them together in a force diagram
Each force must be considered separately when analysing the motion of a specific object

Key termsNewton's Third Lawaction-reaction pairequal and oppositereaction force

Example

A person sits on a chair. The person pushes down on the chair with their weight (action). The chair pushes up on the person with the normal force (reaction). Both are equal and opposite, but act on different objects.

Think of it like this

Think of a tennis ball bouncing off a wall: the ball pushes on the wall, but the wall pushes back on the ball equally hard, sending it away. Neither force is 'stronger'—they're equal partners.

Common mistake

Do not say action-reaction pairs 'cancel out'. They act on different objects, so they cannot cancel. An object accelerates if the resultant force on that object is non-zero.

Must Know

Acceleration is the rate of change of velocity: a = Δv/t (in m/s²). It can be positive or negative.
Three kinematic equations for constant acceleration: a = Δv/t, v² = u² + 2as (when time is unknown), and s = ut + ½at² (when time is known).
Newton's First Law: an object at rest or moving at constant velocity stays that way unless a resultant force acts on it. Balanced forces mean zero acceleration.
Newton's Second Law: F = ma links resultant force, mass, and acceleration. Greater mass = greater resistance to acceleration. Inertia is this resistance; inertial mass measures it.
Newton's Third Law: forces always act in pairs—equal in magnitude, opposite in direction, acting on different objects. Action-reaction pairs do not cancel because they act on separate objects.
Always identify the resultant force before using F = ma. Always show equations, substitute values with units, and explain which law or equation applies to the situation.

Key termsaccelerationresultant forceNewton's Lawsinertiaaction-reaction pairkinematic equations

That's the notes covered.

Carry on to the next subtopic.