PHYSICS • MOTION • QUICK REVISION
Rainbow 🌈 Mind Map
Graphical Representation of Motion
Learn how displacement, velocity and acceleration change with time through clear graph rules, an interactive graph explorer and a quick quiz.
X-axis: Independent variable
Y-axis: Dependent variable
Slope gives rate of change
Area gives accumulated change
What is a graph?
A graph is a diagram that shows the relationship between two variables. The independent variable is generally placed on the X-axis, while the dependent variable is placed on the Y-axis.
X-axis
In motion graphs, time is usually the independent variable because it
moves forward continuously.
Y-axis
Displacement, velocity or acceleration is plotted here because it
changes with time.
Why are motion graphs useful? They make it easier to
identify rest, uniform motion, acceleration, deceleration and non-uniform
motion at a glance.
Three main motion graphs
Tap a graph type to revise its meaning and common shapes.
Displacement–Time graph: shows how displacement changes
with time.
Body at rest
A horizontal line because displacement remains constant.
Uniform motion
A straight sloping line because equal displacement is covered in
equal time.
Speed increasing
A curve that becomes steeper with time.
Speed decreasing
A curve that becomes less steep with time.
Velocity–Time graph: shows how velocity changes with
time.
Body at rest
The line lies on the time axis because velocity is zero.
Uniform velocity
A horizontal line above or below the time axis.
Uniform acceleration
A straight sloping line with constant slope.
Non-uniform acceleration
A curved line because the slope keeps changing.
Acceleration–Time graph: shows how acceleration changes
with time.
Uniform velocity
The line lies on the time axis because acceleration is zero.
Uniform acceleration
A horizontal line because acceleration remains constant.
Positive acceleration
The graph lies above the time axis.
Negative acceleration
The graph lies below the time axis.
Slope and area rules
These four rules are the heart of motion graphs.
Slope of a displacement–time graph
Velocity = Δdisplacement ÷ Δtime
A steeper line represents a greater speed.
Velocity = Δdisplacement ÷ Δtime
A steeper line represents a greater speed.
Slope of a velocity–time graph
Acceleration = Δvelocity ÷ Δtime
A constant slope means uniform acceleration.
Acceleration = Δvelocity ÷ Δtime
A constant slope means uniform acceleration.
Area under a velocity–time graph
Area = Displacement
Signed area gives displacement; total area can be used for distance when direction is considered carefully.
Area = Displacement
Signed area gives displacement; total area can be used for distance when direction is considered carefully.
Area under an acceleration–time graph
Area = Change in velocity
Add this change to the initial velocity to find the final velocity.
Area = Change in velocity
Add this change to the initial velocity to find the final velocity.
Interactive graph explorer
Choose a situation and watch the graph shape change.
A horizontal displacement–time line means the position is not changing,
so the body is at rest.
Quick check
Tap an answer to check your understanding instantly.
1. Which variable is normally placed on the X-axis in a motion graph?
2. What does the slope of a displacement–time graph give?
3. What does the area under a velocity–time graph give?
Frequently asked questions
What is a graph?
A graph is a diagram that shows the relationship between two variables.
The independent variable is generally placed on the X-axis and the
dependent variable on the Y-axis.
Why is time placed on the X-axis?
Time is treated as the independent variable in motion graphs, while
displacement, velocity or acceleration changes with time.
What are the three main motion graphs?
They are displacement–time, velocity–time and acceleration–time
graphs.
What does the slope of a displacement–time graph show?
It shows velocity. A steeper slope represents a greater speed.
What does the area under a velocity–time graph show?
It gives displacement over the selected time interval.
What does the area under an acceleration–time graph show?
It gives the change in velocity over the selected time interval.
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