Units

What you'll learn

How to use the key SI units in forces and motion.
How units such as m/s, m/s² and N/kg are built from simpler units.
How to keep units correct in calculations.
What the Paper 2 only units Nm and kg m/s mean.

Measurements: numbers need units

In physics, a measurement is not complete unless it has both a number and a unit.

For example, saying a track is “100” long is unclear. Is it 100 m, 100 km, or 100 cm? The unit tells you the scale of the measurement.

Definition

Unit

A unit is an agreed standard used to measure a physical quantity. A physical quantity is something that can be measured, such as mass, distance, time, speed or force.

The main system used in science is the SI system, short for the International System of Units. In this topic, the most important starting units are:

Quantity	Unit name	Unit symbol
mass	kilogram	kg
length or distance	metre	m
time	second	s

Tip

Unit symbols are case-sensitive

Write unit symbols exactly: kg, m and s are lower-case, but newton is N because it is named after a person. Do not add plural letters: write 5 kg, not 5 kgs.

Base units and derived units

Some units are base units, meaning they are basic building blocks. The kilogram, metre and second are base units for this topic.

Other units are derived units, meaning they are made by combining base units. For example, speed uses distance and time, so its unit combines metres and seconds.

Relationship map showing base SI units kg, m and s leading to derived units m/s, m/s², N, N/kg, Nm and kg m/s

Key Idea

Units follow the calculation

When quantities are multiplied or divided, their units are multiplied or divided too. That is why units can help you check whether a calculation makes sense.

Metres per second: m/s

Speed tells you how quickly distance is covered.

The equation is:

average speed = distance moved divided by time taken, $\frac{s}{t}$

If distance is measured in metres and time is measured in seconds, the speed unit is metres per second, written as m/s.

“Per” means “for each”. So 8 m/s means 8 metres for each second.

Example

Calculating average speed

A cyclist travels 120 m in 15 s. Calculate the average speed.

Use average speed = distance moved divided by time taken, so $\frac{s}{t}$ .
Substitute the values with units: $\frac{120\ \text{m}}{15\ \text{s}}$ .
Divide the numbers and the units: $8.0\ \text{m/s}$ .

Common Mistake

s can mean seconds or distance

Plain s after a number means seconds, as in 12 s. But italic $s$ in an equation such as $\frac{s}{t}$ can mean distance or displacement. Use the context carefully.

Metres per second squared: m/s²

Acceleration tells you how quickly velocity changes.

Definition

Acceleration

Acceleration is the change in velocity per second. Its unit is metre per second squared, written as m/s².

The equation is:

acceleration = change in velocity divided by time taken, $\frac{v-u}{t}$

Here, $u$ is the initial velocity and $v$ is the final velocity.

An acceleration of 3 m/s² means the velocity changes by 3 m/s every second.

Example

Calculating acceleration

A car’s velocity increases from 4 m/s to 16 m/s in 6 s. Calculate its acceleration.

Find the change in velocity: $16\ \text{m/s} - 4\ \text{m/s} = 12\ \text{m/s}$ .
Use acceleration = change in velocity divided by time taken: $\frac{v-u}{t}$ .
Substitute and calculate: $\frac{12\ \text{m/s}}{6\ \text{s}} = 2.0\ \text{m/s}^2$ .

Newtons: N

A force is a push or pull that can change an object’s motion, shape or direction. The unit of force is the newton, written N.

The equation connecting force, mass and acceleration is:

force = mass multiplied by acceleration, $\times a$

So a newton is linked to kg and m/s². One newton is the force needed to give a 1 kg mass an acceleration of 1 m/s².

Example

Calculating force in newtons

A trolley of mass 0.60 kg accelerates at 2.5 m/s². Calculate the resultant force.

Use force = mass multiplied by acceleration, so $\times a$ .
Substitute the values with units: $0.60\ \text{kg} \times 2.5\ \text{m/s}^2$ .
Calculate: $1.5\ \text{kg m/s}^2$ .
Use the named unit: 1 kg m/s² is 1 N, so $1.5\ \text{N}$ .

Newtons per kilogram: N/kg

The unit N/kg means newtons per kilogram.

It is used for gravitational field strength, usually given the symbol $g$ .

Definition

Gravitational field strength

Gravitational field strength is the force of gravity on each kilogram of mass. Its unit is N/kg.

The equation is:

weight = mass multiplied by gravitational field strength, $\times g$

Weight is a force, so it is measured in newtons. Mass is measured in kilograms.

Example

Calculating weight using N/kg

An object has a mass of 7.5 kg. The gravitational field strength is 10 N/kg. Calculate its weight.

Use weight = mass multiplied by gravitational field strength, so $\times g$ .
Substitute the values with units: $7.5\ \text{kg} \times 10\ \text{N/kg}$ .
The kg cancels with “per kg”, leaving newtons: $75\ \text{N}$ .

Common Mistake

Mass is not weight

Mass is measured in kg. Weight is a force caused by gravity and is measured in N. An astronaut’s mass is the same on Earth and the Moon, but their weight changes because $g$ changes.

Converting before you calculate

In Edexcel IGCSE Physics calculations, use the correct SI units unless the question clearly says otherwise.

Common conversions include:

1000 g = 1 kg
100 cm = 1 m
1000 m = 1 km

If you forget to convert, the final answer may be wrong even if your formula is correct.

Example

Converting units before using force

A toy car has mass 500 g and accelerates at 3.0 m/s². Calculate the force.

Convert the mass into kilograms: 500 g = 0.500 kg.
Use force = mass multiplied by acceleration: $\times a$ .
Substitute and calculate: $0.500\ \text{kg} \times 3.0\ \text{m/s}^2 = 1.5\ \text{N}$ .

Newton metre and kilogram metre per second

You also need to use two more units: newton metre (Nm) and kilogram metre per second (kg m/s). These are assessed on Paper 2 only.

A moment is the turning effect of a force about a pivot. Its unit is Nm.

The equation is:

moment of a force = force multiplied by perpendicular distance from pivot, $\times d$

Momentum is a measure of how much motion an object has. Its unit is kg m/s.

The equation is:

momentum = mass multiplied by velocity, $\times v$

Example

Using Nm and kg m/s

A force of 8.0 N acts 0.25 m from a pivot. A separate object has mass 0.20 kg and velocity 15 m/s. Calculate the moment and the momentum.

For the turning effect, use $\times d$ with the force and perpendicular distance: $8.0\ \text{N} \times 0.25\ \text{m}$ .
Calculate the moment: $2.0\ \text{Nm}$ .
For the moving object, use $\times v$ : $0.20\ \text{kg} \times 15\ \text{m/s}$ .
Calculate the momentum: $3.0\ \text{kg m/s}$ .

Common Mistake

Nm is not N/m

Nm means newtons multiplied by metres, used for moments. N/m means newtons per metre, a different unit used later for spring stiffness.

Exam technique

In the exam

Check the units before substituting into an equation: convert g to kg, cm to m, and keep time in s unless told otherwise.
Write the correct unit on every numerical answer, using exact symbols such as m/s, m/s², N and N/kg.
For Paper 2 calculations, distinguish carefully between Nm for moments and kg m/s for momentum.

Self review

Check yourself

What is the difference between mass in kg and weight in N?
A velocity changes from 5 m/s to 17 m/s in 4 s. What unit should the acceleration have?
Why does a moment use Nm rather than N/m?

What you'll learn

How to use the key SI units in forces and motion.
How units such as m/s, m/s² and N/kg are built from simpler units.
How to keep units correct in calculations.
What the Paper 2 only units Nm and kg m/s mean.

Measurements: numbers need units

In physics, a measurement is not complete unless it has both a number and a unit.

For example, saying a track is “100” long is unclear. Is it 100 m, 100 km, or 100 cm? The unit tells you the scale of the measurement.

Definition

Unit

A unit is an agreed standard used to measure a physical quantity. A physical quantity is something that can be measured, such as mass, distance, time, speed or force.

The main system used in science is the SI system, short for the International System of Units. In this topic, the most important starting units are:

Quantity	Unit name	Unit symbol
mass	kilogram	kg
length or distance	metre	m
time	second	s

Tip

Unit symbols are case-sensitive

Write unit symbols exactly: kg, m and s are lower-case, but newton is N because it is named after a person. Do not add plural letters: write 5 kg, not 5 kgs.

Base units and derived units

Some units are base units, meaning they are basic building blocks. The kilogram, metre and second are base units for this topic.

Other units are derived units, meaning they are made by combining base units. For example, speed uses distance and time, so its unit combines metres and seconds.

Relationship map showing base SI units kg, m and s leading to derived units m/s, m/s², N, N/kg, Nm and kg m/s

Key Idea

Units follow the calculation

When quantities are multiplied or divided, their units are multiplied or divided too. That is why units can help you check whether a calculation makes sense.

Metres per second: m/s

Speed tells you how quickly distance is covered.

The equation is:

average speed = distance moved divided by time taken, $\frac{s}{t}$

If distance is measured in metres and time is measured in seconds, the speed unit is metres per second, written as m/s.

“Per” means “for each”. So 8 m/s means 8 metres for each second.

Example

Calculating average speed

A cyclist travels 120 m in 15 s. Calculate the average speed.

Use average speed = distance moved divided by time taken, so $\frac{s}{t}$ .
Substitute the values with units: $\frac{120\ \text{m}}{15\ \text{s}}$ .
Divide the numbers and the units: $8.0\ \text{m/s}$ .

Common Mistake

s can mean seconds or distance

Plain s after a number means seconds, as in 12 s. But italic $s$ in an equation such as $\frac{s}{t}$ can mean distance or displacement. Use the context carefully.

Metres per second squared: m/s²

Acceleration tells you how quickly velocity changes.

Definition

Acceleration

Acceleration is the change in velocity per second. Its unit is metre per second squared, written as m/s².

The equation is:

acceleration = change in velocity divided by time taken, $\frac{v-u}{t}$

Here, $u$ is the initial velocity and $v$ is the final velocity.

An acceleration of 3 m/s² means the velocity changes by 3 m/s every second.

Example

Calculating acceleration

A car’s velocity increases from 4 m/s to 16 m/s in 6 s. Calculate its acceleration.

Find the change in velocity: $16\ \text{m/s} - 4\ \text{m/s} = 12\ \text{m/s}$ .
Use acceleration = change in velocity divided by time taken: $\frac{v-u}{t}$ .
Substitute and calculate: $\frac{12\ \text{m/s}}{6\ \text{s}} = 2.0\ \text{m/s}^2$ .

Newtons: N

A force is a push or pull that can change an object’s motion, shape or direction. The unit of force is the newton, written N.

The equation connecting force, mass and acceleration is:

force = mass multiplied by acceleration, $\times a$

So a newton is linked to kg and m/s². One newton is the force needed to give a 1 kg mass an acceleration of 1 m/s².

Example

Calculating force in newtons

A trolley of mass 0.60 kg accelerates at 2.5 m/s². Calculate the resultant force.

Use force = mass multiplied by acceleration, so $\times a$ .
Substitute the values with units: $0.60\ \text{kg} \times 2.5\ \text{m/s}^2$ .
Calculate: $1.5\ \text{kg m/s}^2$ .
Use the named unit: 1 kg m/s² is 1 N, so $1.5\ \text{N}$ .

Newtons per kilogram: N/kg

The unit N/kg means newtons per kilogram.

It is used for gravitational field strength, usually given the symbol $g$ .

Definition

Gravitational field strength

Gravitational field strength is the force of gravity on each kilogram of mass. Its unit is N/kg.

The equation is:

weight = mass multiplied by gravitational field strength, $\times g$

Weight is a force, so it is measured in newtons. Mass is measured in kilograms.

Example

Calculating weight using N/kg

An object has a mass of 7.5 kg. The gravitational field strength is 10 N/kg. Calculate its weight.

Use weight = mass multiplied by gravitational field strength, so $\times g$ .
Substitute the values with units: $7.5\ \text{kg} \times 10\ \text{N/kg}$ .
The kg cancels with “per kg”, leaving newtons: $75\ \text{N}$ .

Common Mistake

Mass is not weight

Mass is measured in kg. Weight is a force caused by gravity and is measured in N. An astronaut’s mass is the same on Earth and the Moon, but their weight changes because $g$ changes.

Converting before you calculate

In Edexcel IGCSE Physics calculations, use the correct SI units unless the question clearly says otherwise.

Common conversions include:

1000 g = 1 kg
100 cm = 1 m
1000 m = 1 km

If you forget to convert, the final answer may be wrong even if your formula is correct.

Example

Converting units before using force

A toy car has mass 500 g and accelerates at 3.0 m/s². Calculate the force.

Convert the mass into kilograms: 500 g = 0.500 kg.
Use force = mass multiplied by acceleration: $\times a$ .
Substitute and calculate: $0.500\ \text{kg} \times 3.0\ \text{m/s}^2 = 1.5\ \text{N}$ .

Newton metre and kilogram metre per second

You also need to use two more units: newton metre (Nm) and kilogram metre per second (kg m/s). These are assessed on Paper 2 only.

A moment is the turning effect of a force about a pivot. Its unit is Nm.

The equation is:

moment of a force = force multiplied by perpendicular distance from pivot, $\times d$

Momentum is a measure of how much motion an object has. Its unit is kg m/s.

The equation is:

momentum = mass multiplied by velocity, $\times v$

Example

Using Nm and kg m/s

A force of 8.0 N acts 0.25 m from a pivot. A separate object has mass 0.20 kg and velocity 15 m/s. Calculate the moment and the momentum.

For the turning effect, use $\times d$ with the force and perpendicular distance: $8.0\ \text{N} \times 0.25\ \text{m}$ .
Calculate the moment: $2.0\ \text{Nm}$ .
For the moving object, use $\times v$ : $0.20\ \text{kg} \times 15\ \text{m/s}$ .
Calculate the momentum: $3.0\ \text{kg m/s}$ .

Common Mistake

Nm is not N/m

Nm means newtons multiplied by metres, used for moments. N/m means newtons per metre, a different unit used later for spring stiffness.

Exam technique

In the exam

Check the units before substituting into an equation: convert g to kg, cm to m, and keep time in s unless told otherwise.
Write the correct unit on every numerical answer, using exact symbols such as m/s, m/s², N and N/kg.
For Paper 2 calculations, distinguish carefully between Nm for moments and kg m/s for momentum.

Self review

Check yourself

What is the difference between mass in kg and weight in N?
A velocity changes from 5 m/s to 17 m/s in 4 s. What unit should the acceleration have?
Why does a moment use Nm rather than N/m?

What you'll learn

Measurements: numbers need units

Base units and derived units

Metres per second: m/s

Metres per second squared: m/s²

Newtons: N

Newtons per kilogram: N/kg

Converting before you calculate

Newton metre and kilogram metre per second

Review Units by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Units

What you'll learn

Measurements: numbers need units

Base units and derived units

Metres per second: m/s

Metres per second squared: m/s²

Newtons: N

Newtons per kilogram: N/kg

Converting before you calculate

Newton metre and kilogram metre per second

Review Units by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Units

What you'll learn

Measurements: numbers need units

Base units and derived units

Metres per second: m/s

Metres per second squared: m/s²

Newtons: N

Newtons per kilogram: N/kg

Converting before you calculate

Newton metre and kilogram metre per second

Review Units by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Units Revision Guide

Units

What you'll learn

Measurements: numbers need units

Base units and derived units

Metres per second: m/s

Metres per second squared: m/s²

Newtons: N

Newtons per kilogram: N/kg

Converting before you calculate

Newton metre and kilogram metre per second

Review Units by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Units Revision Guide