Motion

What you'll learn

How to measure distance and time, then calculate speed.
How to tell the difference between scalar and vector quantities in motion.
How to interpret distance–time graphs and velocity–time graphs.
How acceleration and kinetic energy link to moving objects.

Motion starts with position

An object is in motion when its position changes compared with a chosen reference point. A reference point is something you compare the object’s position with, such as a lamp post, the start line, or the laboratory bench.

Motion is not just about “how fast”. Direction matters too, especially when an object turns around or moves backwards.

Key Idea

Motion is measured relative to something

To describe motion clearly, you need to know how far, how long, and sometimes in which direction.

Measuring distance and time

Distance is how far an object travels along its path. In school practical work, you might measure it using a ruler, tape measure, metre rule, or trundle wheel.

Time is how long the motion takes. You might measure it using a stopwatch, light gate, data logger, ticker timer, or video analysis.

In an acceleration investigation, a trolley can roll down a ramp through two light gates. The distance between the gates is measured with a ruler or tape, and the data logger records times very accurately.

Trolley on a ramp passing through two light gates connected to a data logger, with distance between gates labelled

Tip

Reducing measurement uncertainty

Use light gates or video analysis instead of a hand-held stopwatch when timing is very short.
Measure distance from the same point on the object each time.
Repeat readings and calculate a mean if the motion is repeatable.

Speed

Definition

Speed

Speed is the rate at which distance is travelled. It tells you how much distance is covered per second.

The equation is:

travelled=speed×time\text{distance travelled} = \text{speed} \times \text{time}

You must be able to recall and apply this equation. Rearranged for speed:

travelledtime\text{speed} = \frac{\text{distance travelled}}{\text{time}}

Speed is measured in metres per second (m/s) when distance is in metres and time is in seconds.

Example

Calculating speed

A cyclist travels 180 m in 12 s. Calculate the cyclist’s speed.

The unknown is speed, so use $\frac{s}{t}$ , where $s$ is distance and $t$ is time.
Substitute the values with units: $\frac{180\ \text{m}}{12\ \text{s}}$ .
Calculate the result: $15\ \text{m/s}$ .

Uniform and non-uniform motion

Uniform motion means the object moves at a constant speed. It covers equal distances in equal times.

Non-uniform motion means the speed changes. For example, a runner may start slowly, speed up, then slow down near the finish.

For non-uniform motion, you can calculate average speed:

time\text{average speed} = \frac{\text{total distance}}{\text{total time}}

Example

Average speed for a two-part journey

A student walks 90 m in 60 s, then jogs 150 m in 50 s. Calculate the average speed for the whole journey.

Add the distances: total distance = 90 m + 150 m = 240 m.
Add the times: total time = 60 s + 50 s = 110 s.
Use average speed: $\frac{240\ \text{m}}{110\ \text{s}} = 2.18\ \text{m/s}$ , which is about 2.2 m/s.

Converting units

GCSE motion calculations usually use SI units: metres, seconds, metres per second, and metres per second squared.

Common conversions include:

1 km = 1000 m
1 hour = 3600 s
1 minute = 60 s

Example

Converting kilometres per hour to metres per second

Convert 54 km/h into m/s.

Convert kilometres to metres and hours to seconds:
$s54\ \text{km/h} = \frac{54\,000\ \text{m}}{3600\ \text{s}}$
Divide distance by time:
$0003600=15\frac{54\,000}{3600} = 15$
Give the converted speed: 54 km/h = 15 m/s.

Tip

Quick km/h to m/s conversion

To convert from km/h to m/s, divide by 3.6. To convert from m/s to km/h, multiply by 3.6.

Scalars and vectors

Definition

Scalar and vector quantities

A scalar quantity has size only, such as distance, speed, mass, time, or energy.
A vector quantity has size and direction, such as displacement, velocity, acceleration, or force.

Distance is a scalar. It is the total length of the path travelled.

Displacement is a vector. It is the straight-line change in position from start to finish, including direction.

Speed is a scalar. Velocity is a vector: it is speed in a stated direction.

Example

Distance and displacement

A student walks 30 m east, then 10 m west. The journey takes 20 s.

Add the path lengths to find distance: distance = 30 m + 10 m = 40 m.
Compare the start and finish positions: the student ends up 20 m east of the start, so displacement = 20 m east.
Average speed uses distance: $\frac{40\ \text{m}}{20\ \text{s}} = 2.0\ \text{m/s}$ .
Average velocity uses displacement: average velocity = 1.0 m/s east.

Common Mistake

Thinking velocity must be positive

Velocity can be negative if the object moves in the opposite direction to the direction chosen as positive. Negative velocity does not mean negative speed.

Acceleration

Definition

Acceleration

Acceleration is the rate of change of velocity. It tells you how quickly velocity changes each second.

The equation is:

\frac{\Delta v}{t} = \frac{v-u}{t}

where:

$a$ is acceleration in m/s²
$u$ is initial velocity in m/s
$v$ is final velocity in m/s
$t$ is time in s

This is a recall and apply equation, so you should learn it.

If an object speeds up, its acceleration is in the same direction as its motion. If it slows down, its acceleration is opposite to its motion; this is often called deceleration.

Example

Calculating acceleration

A car slows from 18 m/s to 6 m/s in 4 s. Taking the original direction as positive, calculate its acceleration.

Identify the velocities: $18\ \text{m/s}$ and $6\ \text{m/s}$ .
Substitute into the acceleration equation:
$\frac{6\ \text{m/s} - 18\ \text{m/s}}{4\ \text{s}}$
Calculate the change in velocity and divide by time: $-3.0\ \text{m/s}^2$ .
The negative sign means the acceleration is opposite to the original direction of motion.

Uniform acceleration without time

Sometimes a question gives distance, initial velocity, final velocity, and acceleration, but not time. For uniform acceleration — acceleration that stays constant — you can use:

v^2 - u^2 = 2as

where $s$ is the distance or displacement along the line of motion.

In the OCR wording, this is an apply equation rather than a recall equation, so you need to be able to use it when it is provided, but it is still worth recognising.

Example

Finding final velocity with uniform acceleration

A trolley starts from rest and accelerates uniformly at 2.0 m/s² for a distance of 4.0 m. Calculate its final velocity.

Choose the equation because time is not given: $v^2 - u^2 = 2as$ .
Substitute $0\ \text{m/s}$ , $2.0\ \text{m/s}^2$ , and $4.0\ \text{m}$ :
$v2−02=2×2.0×4.0v^2 - 0^2 = 2 \times 2.0 \times 4.0$
Calculate $v^2$ : $v^2 = 16$ .
Take the square root: $4.0\ \text{m/s}$ .

Common Mistake

When this equation applies

Only use $v^2 - u^2 = 2as$ when acceleration is constant and the motion is along one straight line.

Motion graphs

Graphs help you see patterns in motion quickly. In both main graph types, time goes on the horizontal axis. The vertical axis tells you what kind of graph it is.

Distance-time graph and velocity-time graph showing gradients, constant speed, stationary sections, acceleration, deceleration and area under a velocity-time graph

Distance–time graphs

On a distance–time graph, the gradient gives speed.

A straight sloping line means constant speed.
A horizontal line means the object is stationary.
A steeper line means a greater speed.
A curve that gets steeper means the object is speeding up.

Example

Finding speed from a distance-time graph

A straight section of a distance–time graph goes from 20 m at 10 s to 100 m at 30 s. Calculate the speed.

Find the change in distance: 100 m - 20 m = 80 m.
Find the change in time: 30 s - 10 s = 20 s.
Calculate the gradient: $\frac{80\ \text{m}}{20\ \text{s}} = 4.0\ \text{m/s}$ .

Velocity–time graphs

On a velocity–time graph, the gradient gives acceleration.

A horizontal line means constant velocity.
A line sloping upwards means positive acceleration.
A line sloping downwards means negative acceleration or deceleration.
A line on the time axis means zero velocity, so the object is stationary.

Common Mistake

Horizontal line on a velocity-time graph

A horizontal line on a velocity–time graph does not mean stationary unless it is at zero velocity. It usually means constant velocity.

Area under a velocity–time graph

This part is Higher Tier only in the OCR topic content.

For a velocity–time graph, the enclosed area under the line gives the distance travelled when velocity is positive. If the graph goes below the time axis, the signed area represents displacement, so direction matters.

Example

Finding distance from a velocity-time graph

A car accelerates from 0 to 10 m/s in 5 s, then continues at 10 m/s for 8 s. Calculate the distance travelled.

Split the area under the graph into a triangle and a rectangle.
Triangle during acceleration:
$m\text{area} = \frac{1}{2} \times 5\ \text{s} \times 10\ \text{m/s} = 25\ \text{m}$
Rectangle during constant velocity:
$m\text{area} = 8\ \text{s} \times 10\ \text{m/s} = 80\ \text{m}$
Add the areas: total distance = 25 m + 80 m = 105 m.

Kinetic energy

Definition

Kinetic energy

Kinetic energy is the energy an object has because it is moving.

The equation is:

Ek=12mv2E_k = \frac{1}{2}mv^2

where:

$E_k$ is kinetic energy in joules (J)
$m$ is mass in kilograms (kg)
$v$ is speed in m/s

This is a recall and apply equation. Notice that speed is squared, so doubling speed makes kinetic energy four times bigger.

Example

Calculating kinetic energy

A 0.50 kg ball moves at 12 m/s. Calculate its kinetic energy.

Use $Ek=12mv2E_k = \frac{1}{2}mv^2$ .
Substitute the values:
$Ek=12×0.50×122E_k = \frac{1}{2} \times 0.50 \times 12^2$
Square the speed and calculate:
$JE_k = 0.25 \times 144 = 36\ \text{J}$

Exam technique

In the exam

Check units first: convert distances to metres and times to seconds before calculating.
Decide whether the quantity needs direction: speed and distance are scalars; velocity and displacement are vectors.
On graphs, use gradient for rate of change; for Higher Tier velocity–time graphs, use area to find distance or displacement.

Self review

Check yourself

A runner travels 200 m in 25 s. What is their average speed?
What is the difference between distance and displacement for a journey that ends back at the start?
On a velocity–time graph, what does a downward sloping line show?

What you'll learn

How to measure distance and time, then calculate speed.
How to tell the difference between scalar and vector quantities in motion.
How to interpret distance–time graphs and velocity–time graphs.
How acceleration and kinetic energy link to moving objects.

Motion starts with position

Motion is not just about “how fast”. Direction matters too, especially when an object turns around or moves backwards.

Key Idea

Motion is measured relative to something

To describe motion clearly, you need to know how far, how long, and sometimes in which direction.

Measuring distance and time

Distance is how far an object travels along its path. In school practical work, you might measure it using a ruler, tape measure, metre rule, or trundle wheel.

Time is how long the motion takes. You might measure it using a stopwatch, light gate, data logger, ticker timer, or video analysis.

Trolley on a ramp passing through two light gates connected to a data logger, with distance between gates labelled

Tip

Reducing measurement uncertainty

Use light gates or video analysis instead of a hand-held stopwatch when timing is very short.
Measure distance from the same point on the object each time.
Repeat readings and calculate a mean if the motion is repeatable.

Speed

Definition

Speed

Speed is the rate at which distance is travelled. It tells you how much distance is covered per second.

The equation is:

travelled=speed×time\text{distance travelled} = \text{speed} \times \text{time}

You must be able to recall and apply this equation. Rearranged for speed:

travelledtime\text{speed} = \frac{\text{distance travelled}}{\text{time}}

Speed is measured in metres per second (m/s) when distance is in metres and time is in seconds.

Example

Calculating speed

A cyclist travels 180 m in 12 s. Calculate the cyclist’s speed.

The unknown is speed, so use $\frac{s}{t}$ , where $s$ is distance and $t$ is time.
Substitute the values with units: $\frac{180\ \text{m}}{12\ \text{s}}$ .
Calculate the result: $15\ \text{m/s}$ .

Uniform and non-uniform motion

Uniform motion means the object moves at a constant speed. It covers equal distances in equal times.

Non-uniform motion means the speed changes. For example, a runner may start slowly, speed up, then slow down near the finish.

For non-uniform motion, you can calculate average speed:

time\text{average speed} = \frac{\text{total distance}}{\text{total time}}

Example

Average speed for a two-part journey

A student walks 90 m in 60 s, then jogs 150 m in 50 s. Calculate the average speed for the whole journey.

Add the distances: total distance = 90 m + 150 m = 240 m.
Add the times: total time = 60 s + 50 s = 110 s.
Use average speed: $\frac{240\ \text{m}}{110\ \text{s}} = 2.18\ \text{m/s}$ , which is about 2.2 m/s.

Converting units

GCSE motion calculations usually use SI units: metres, seconds, metres per second, and metres per second squared.

Common conversions include:

1 km = 1000 m
1 hour = 3600 s
1 minute = 60 s

Example

Converting kilometres per hour to metres per second

Convert 54 km/h into m/s.

Convert kilometres to metres and hours to seconds:
$s54\ \text{km/h} = \frac{54\,000\ \text{m}}{3600\ \text{s}}$
Divide distance by time:
$0003600=15\frac{54\,000}{3600} = 15$
Give the converted speed: 54 km/h = 15 m/s.

Tip

Quick km/h to m/s conversion

To convert from km/h to m/s, divide by 3.6. To convert from m/s to km/h, multiply by 3.6.

Scalars and vectors

Definition

Scalar and vector quantities

A scalar quantity has size only, such as distance, speed, mass, time, or energy.
A vector quantity has size and direction, such as displacement, velocity, acceleration, or force.

Distance is a scalar. It is the total length of the path travelled.

Displacement is a vector. It is the straight-line change in position from start to finish, including direction.

Speed is a scalar. Velocity is a vector: it is speed in a stated direction.

Example

Distance and displacement

A student walks 30 m east, then 10 m west. The journey takes 20 s.

Add the path lengths to find distance: distance = 30 m + 10 m = 40 m.
Compare the start and finish positions: the student ends up 20 m east of the start, so displacement = 20 m east.
Average speed uses distance: $\frac{40\ \text{m}}{20\ \text{s}} = 2.0\ \text{m/s}$ .
Average velocity uses displacement: average velocity = 1.0 m/s east.

Common Mistake

Thinking velocity must be positive

Velocity can be negative if the object moves in the opposite direction to the direction chosen as positive. Negative velocity does not mean negative speed.

Acceleration

Definition

Acceleration

Acceleration is the rate of change of velocity. It tells you how quickly velocity changes each second.

The equation is:

\frac{\Delta v}{t} = \frac{v-u}{t}

where:

$a$ is acceleration in m/s²
$u$ is initial velocity in m/s
$v$ is final velocity in m/s
$t$ is time in s

This is a recall and apply equation, so you should learn it.

If an object speeds up, its acceleration is in the same direction as its motion. If it slows down, its acceleration is opposite to its motion; this is often called deceleration.

Example

Calculating acceleration

A car slows from 18 m/s to 6 m/s in 4 s. Taking the original direction as positive, calculate its acceleration.

Identify the velocities: $18\ \text{m/s}$ and $6\ \text{m/s}$ .
Substitute into the acceleration equation:
$\frac{6\ \text{m/s} - 18\ \text{m/s}}{4\ \text{s}}$
Calculate the change in velocity and divide by time: $-3.0\ \text{m/s}^2$ .
The negative sign means the acceleration is opposite to the original direction of motion.

Uniform acceleration without time

Sometimes a question gives distance, initial velocity, final velocity, and acceleration, but not time. For uniform acceleration — acceleration that stays constant — you can use:

v^2 - u^2 = 2as

where $s$ is the distance or displacement along the line of motion.

In the OCR wording, this is an apply equation rather than a recall equation, so you need to be able to use it when it is provided, but it is still worth recognising.

Example

Finding final velocity with uniform acceleration

A trolley starts from rest and accelerates uniformly at 2.0 m/s² for a distance of 4.0 m. Calculate its final velocity.

Choose the equation because time is not given: $v^2 - u^2 = 2as$ .
Substitute $0\ \text{m/s}$ , $2.0\ \text{m/s}^2$ , and $4.0\ \text{m}$ :
$v2−02=2×2.0×4.0v^2 - 0^2 = 2 \times 2.0 \times 4.0$
Calculate $v^2$ : $v^2 = 16$ .
Take the square root: $4.0\ \text{m/s}$ .

Common Mistake

When this equation applies

Only use $v^2 - u^2 = 2as$ when acceleration is constant and the motion is along one straight line.

Motion graphs

Graphs help you see patterns in motion quickly. In both main graph types, time goes on the horizontal axis. The vertical axis tells you what kind of graph it is.

Distance-time graph and velocity-time graph showing gradients, constant speed, stationary sections, acceleration, deceleration and area under a velocity-time graph

Distance–time graphs

On a distance–time graph, the gradient gives speed.

A straight sloping line means constant speed.
A horizontal line means the object is stationary.
A steeper line means a greater speed.
A curve that gets steeper means the object is speeding up.

Example

Finding speed from a distance-time graph

A straight section of a distance–time graph goes from 20 m at 10 s to 100 m at 30 s. Calculate the speed.

Find the change in distance: 100 m - 20 m = 80 m.
Find the change in time: 30 s - 10 s = 20 s.
Calculate the gradient: $\frac{80\ \text{m}}{20\ \text{s}} = 4.0\ \text{m/s}$ .

Velocity–time graphs

On a velocity–time graph, the gradient gives acceleration.

A horizontal line means constant velocity.
A line sloping upwards means positive acceleration.
A line sloping downwards means negative acceleration or deceleration.
A line on the time axis means zero velocity, so the object is stationary.

Common Mistake

Horizontal line on a velocity-time graph

A horizontal line on a velocity–time graph does not mean stationary unless it is at zero velocity. It usually means constant velocity.

Area under a velocity–time graph

This part is Higher Tier only in the OCR topic content.

Example

Finding distance from a velocity-time graph

A car accelerates from 0 to 10 m/s in 5 s, then continues at 10 m/s for 8 s. Calculate the distance travelled.

Split the area under the graph into a triangle and a rectangle.
Triangle during acceleration:
$m\text{area} = \frac{1}{2} \times 5\ \text{s} \times 10\ \text{m/s} = 25\ \text{m}$
Rectangle during constant velocity:
$m\text{area} = 8\ \text{s} \times 10\ \text{m/s} = 80\ \text{m}$
Add the areas: total distance = 25 m + 80 m = 105 m.

Kinetic energy

Definition

Kinetic energy

Kinetic energy is the energy an object has because it is moving.

The equation is:

Ek=12mv2E_k = \frac{1}{2}mv^2

where:

$E_k$ is kinetic energy in joules (J)
$m$ is mass in kilograms (kg)
$v$ is speed in m/s

This is a recall and apply equation. Notice that speed is squared, so doubling speed makes kinetic energy four times bigger.

Example

Calculating kinetic energy

A 0.50 kg ball moves at 12 m/s. Calculate its kinetic energy.

Use $Ek=12mv2E_k = \frac{1}{2}mv^2$ .
Substitute the values:
$Ek=12×0.50×122E_k = \frac{1}{2} \times 0.50 \times 12^2$
Square the speed and calculate:
$JE_k = 0.25 \times 144 = 36\ \text{J}$

Exam technique

In the exam

Check units first: convert distances to metres and times to seconds before calculating.
Decide whether the quantity needs direction: speed and distance are scalars; velocity and displacement are vectors.
On graphs, use gradient for rate of change; for Higher Tier velocity–time graphs, use area to find distance or displacement.

Self review

Check yourself

A runner travels 200 m in 25 s. What is their average speed?
What is the difference between distance and displacement for a journey that ends back at the start?
On a velocity–time graph, what does a downward sloping line show?

What you'll learn

Motion starts with position

Measuring distance and time

Speed

Uniform and non-uniform motion

Converting units

Scalars and vectors

Acceleration

Uniform acceleration without time

Motion graphs

Distance–time graphs

Velocity–time graphs

Area under a velocity–time graph

Kinetic energy

Recap questions

Review Motion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

Motion

What you'll learn

Motion starts with position

Measuring distance and time

Speed

Uniform and non-uniform motion

Converting units

Scalars and vectors

Acceleration

Uniform acceleration without time

Motion graphs

Distance–time graphs

Velocity–time graphs

Area under a velocity–time graph

Kinetic energy

Recap questions

Review Motion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

Motion

What you'll learn

Motion starts with position

Measuring distance and time

Speed

Uniform and non-uniform motion

Converting units

Scalars and vectors

Acceleration

Uniform acceleration without time

Motion graphs

Distance–time graphs

Velocity–time graphs

Area under a velocity–time graph

Kinetic energy

Recap questions

Review Motion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

Motion Revision Guide

Motion

What you'll learn

Motion starts with position

Measuring distance and time

Speed

Uniform and non-uniform motion

Converting units

Scalars and vectors

Acceleration

Uniform acceleration without time

Motion graphs

Distance–time graphs

Velocity–time graphs

Area under a velocity–time graph

Kinetic energy

Recap questions

Review Motion by teaching Genie

Recap your knowledge with an interactive lesson

Put it into practice with exam-style questions

Remember key concepts with flashcards

Motion Revision Guide