Plotting kinematics graphs from data
Key idea: Plot displacement–time and velocity–time graphs accurately, choose suitable scales and decide whether points need exact connections or a best-fit trend.
Continue where you stopped
The core idea
On this page
Learning objectives
- State what speed means
- State what velocity means, including its direction
- Calculate average speed from total distance and total time
- Calculate acceleration as change in velocity divided by time taken
- State what uniform acceleration means
- Interpret examples of non-uniform acceleration
- Plot and interpret displacement–time and velocity–time graphs in one dimension
- Deduce rest and uniform or non-uniform velocity from a displacement–time graph
- Deduce rest, uniform velocity and uniform or non-uniform acceleration from a velocity–time graph
- Use signed area under a velocity–time graph to determine displacement
- Recall constant free-fall acceleration near Earth as approximately 10 m/s²
1. Definitions
A kinematics graph shows how displacement or velocity changes with time. Time goes on the horizontal axis. The vertical axis is usually displacement, s, or velocity, v.
Revise displacement and velocity and how to read gradients. Negative values show direction; do not discard their signs.
2. Key Ideas
- Label both axes with quantity and unit, such as t/s and v/m s⁻¹.
- Choose simple, even scales that use at least half the available grid in each direction.
- Plot each point as a small, clear cross.
- Connect or fit the points using the information given in the question.
- Recheck one awkward coordinate against both scales.
Good scale intervals usually follow 1, 2 or 5 multiplied by a power of ten. Do not change scale part-way along an axis.
3. Detailed Explanations
The correct line depends on what the data represent.
| Data in the question | What to draw | Why |
|---|---|---|
| Exact values describing consecutive stages of motion | Join consecutive points with the stated straight lines or smooth curve | The connections are part of the motion model |
| Experimental measurements with scatter | Draw the requested best-fit straight line or smooth curve | The aim is to show the overall trend, not every random variation |
Do not automatically draw dot-to-dot lines through scattered experimental readings. Equally, do not replace an exact piecewise motion graph with a best-fit line.
Interpreting the finished graph
| Graph | Gradient | Useful shape clues |
|---|---|---|
| displacement–time | velocity | horizontal means rest; a constant gradient means constant velocity |
| velocity–time | acceleration | horizontal means constant velocity; a constant gradient means constant acceleration |
Signed area under a velocity–time graph gives displacement. Revise the area method separately.
Exact velocity–time data for uniform acceleration
Velocity values at zero, one, two and three seconds are stated to be joined by straight lines, producing a straight line from zero to six metres per second.
Scroll across the graph to read all labels.
View figure data
| Time (s) | Exact motion data |
|---|---|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
4. Common Mistakes
- Choosing a scale that wastes most of the grid or changes increment partway along an axis.
- Drawing a dot-to-dot zigzag through experimental measurements when a best-fit trend is required.
- Interpreting gradient or area before checking what the two axes represent and whether direction is signed.
5. Exam Tips
- Label each axis with quantity and unit, use a simple uniform scale and plot small precise crosses.
- Decide from the data source whether the graph represents an exact piecewise motion or noisy experimental measurements.
- Show the triangle used for a gradient across a large interval and keep its units visible.
6. Worked Examples
Modelled example 1
Exact displacement–time record
Problem
| t/s | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| s/m | 0 | 2 | 4 | 4 | 4 |
Join consecutive points with straight lines. Describe the motion and find the velocity from 0–2 s.
Study the worked solution
Plot the exact record
Method
Label t/s and s/m, plot small crosses, and join consecutive points as instructed.Reason
The values describe exact motion stages, so a best-fit trend would change the stated record.Working
The first three points form a rising straight line; the final three include a horizontal section from 2–4 s.Interpret the two sections
Method
Use displacement–time gradient as velocity.Reason
A constant displacement has zero gradient.Working
v₀₋₂ = (4-0)/(2-0) = 2.0 m s⁻¹; v₂₋₄ = 0
Guided practice 2
Exact velocity–time record
Problem
| t/s | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| v/m s⁻¹ | 6 | 2 | -2 | -6 |
Velocity changes uniformly between readings. Find the acceleration and when the object changes direction.
Use the exact straight-line record
Hints
Hint 1: use a large gradient triangle
Hint 2: find the zero crossing
View solution step by step
Calculate the exact gradient
Method
Use well-separated endpoints on the straight line.Reason
The stated uniform change makes the gradient constant.Working
a = (-6-6)/(6-0) = -2.0 m s⁻²Locate the direction change
Method
Find where the line crosses the time axis.Reason
Velocity changes sign after passing through zero.Working
The line reaches v = 0 at t = 3.0 s.
Common misconception 3
Experimental readings with scatter
Learner response
Match the line to the data source
View solution step by step
Choose a best-fit trend
Method
Draw a straight line with a reasonable balance of points above and below.Reason
Scatter reflects measurement variation; a zigzag implies unsupported changes between every reading.Working
Use two well-separated points on the fitted line to calculate its gradient.Treat the intercept as evidence-dependent
Method
Do not force the line through the origin automatically.Reason
The origin is justified only when the data or physical setup supports a zero intercept.Working
The fitted intercept should follow the observed trend and experimental model.
Examiner practice 4
Exact-data plotting decisions
Examination question
Exact motion data are (t, v) = (0,-4),(2,0),(4,4),(6,8), with time in seconds and velocity in m s⁻¹. State suitable axis labels, describe how the points should be connected, and calculate the acceleration. [5 marks]
Include graph conventions and interpretation
View solution step by step
Label both axes
2 marksMethod
Use t/s horizontally and v/m s⁻¹ vertically.Reason
Quantity and unit are both required to interpret coordinates and gradient units.Working
The velocity scale must include the negative value -4 m s⁻¹.Connect the exact points
1 markMethod
Join consecutive points with straight lines.Reason
The values are stated as exact motion data and lie on one straight trend.Working
Do not replace them with an experimental best-fit line.Calculate the acceleration
2 marksMethod
Use the velocity–time gradient.Reason
The straight line represents uniform acceleration.Working
a = (8-(-4))/(6-0) = 2.0 m s⁻²
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Self-mark the two labelled axes, connection decision and two-part gradient calculation.
Challenge 5
The data origin changes the line decision
Method transfer
Compare both evidence models
Hints
Hint 1: exact record
Hint 2: experimental record
View solution step by step
Treat the exact stage as stated motion
Method
Plot and connect the point according to the specified stage sequence.Reason
Its deviation represents a real commanded change, not random measurement scatter.Working
The piecewise exact graph changes shape at that point.Treat the experimental point as evidence
Method
Retain the plotted reading but use the requested best-fit trend and consider whether it is anomalous.Reason
One measurement may reflect random variation; repeats and the overall pattern determine its influence.Working
Do not silently delete it or force the fitted line through it.
Further mistakes to diagnose
- Omitting units or putting the wrong quantity on an axis.
- Using an awkward or uneven scale.
- Drawing thick points that hide their coordinates.
- Forcing a best-fit line through every experimental point.
- Drawing a best-fit trend through exact stages that should be joined in order.
- Reading a negative velocity as a negative speed rather than motion in the opposite direction.
7. Mind Stretchers
Mind stretcher 1: Exact record or experimental scatter?Extension
Before using the interactive, predict how one changed data point should affect an exact motion record and an experimental best-fit trend. Explain why the decision depends on the data origin.
Show answer
In an exact record, the changed point changes the stated motion stage and the connected graph. In experimental data, it may shift a best-fit trend slightly or be treated as a possible anomalous reading after repeats and measurement limitations are considered. The point should still be plotted; its influence depends on what produced it.
Interactive check
Use the explorer to connect graph shape with motion. Predict the gradient, direction and signed area before revealing the explanation.
Concept Explorer: Kinematics Graph Relationships
Switch graph-shape presets, move the time marker, and connect slope/area ideas across position-time, velocity-time, and acceleration-time graphs.
- Gradient Interpretation
- Signed Area
- Direction From Velocity
- Graph Translation
Open the full Kinematics Graph Explorer for a larger workspace.
Continue with the next resource in this course.
Course and syllabus information
- Course
- SEC G3 Physics
- Edition
- SEC G3 Physics 2027