Understanding motion
How to read a distance-time graph without guessing
A rising line is not a hill. Read the axes, describe each part of the journey and use changes in distance and time to calculate speed.
Start by saying what the axes measure
Ask your child to complete two sentences before calculating anything: the horizontal axis measures what, and the vertical axis measures what? A distance-time graph records a relationship between measurements. It is not a drawing of the road. An upward-sloping section does not mean that someone is walking uphill, and a horizontal section does not mean that the road is flat.
For the worked example below, the vertical axis is cumulative distance travelled in metres, and the horizontal axis is elapsed time in seconds. That choice matters. A graph labelled distance from home can fall as someone returns home; cumulative distance travelled cannot decrease. If a worksheet uses the shorter label distance, read its description before deciding which meaning is intended.
The hero is an AI-generated illustration of fictional people, not a photograph of our staff, pupils or a school. The numerical journey below is an original practice example, not measured student data.
Read one journey in four parts
Imagine a pupil moving along a straight path, pausing to check a bag and then continuing at a jog before slowing down. Plot these points on squared paper: at 0 seconds, 0 metres; at 10 seconds, 20 metres; at 25 seconds, 20 metres; at 45 seconds, 80 metres; at 60 seconds, 95 metres. Join consecutive points with straight lines. We are deliberately modelling constant speed within each moving section.
Before finding any speed, ask your child to tell the story using the table. Which interval is a pause? During which interval is the most distance covered? Those are different questions from which interval is fastest. Separating them helps reveal whether an error comes from reading the graph or doing the arithmetic.
| Time interval | Distance added | What happens |
|---|---|---|
| 0 to 10 seconds | 20 metres | Walking steadily |
| 10 to 25 seconds | 0 metres | Stationary for 15 seconds |
| 25 to 45 seconds | 60 metres | Jogging at a greater steady speed |
| 45 to 60 seconds | 15 metres | Walking more slowly |
Calculate the change, not just the final reading
On a straight section, speed is the distance added divided by the time taken. Between 25 and 45 seconds, the distance changes from 20 to 80 metres. The calculation is therefore (80 minus 20) divided by (45 minus 25), giving 60 divided by 20 = 3 metres per second. Dividing 80 by 45 would mix earlier movement and the pause into a question about this section.
The four section speeds are 2, 0, 3 and 1 metres per second. Ask your child to point to both readings used in each subtraction. Writing the units beside the numbers is a useful check: metres divided by seconds gives metres per second. If an axis uses minutes or kilometres, keep the units consistent before comparing answers.
For the whole journey, the average speed is 95 metres divided by 60 seconds, approximately 1.58 metres per second. The pause is included because the question covers the whole elapsed journey. Taking the simple average of the four section speeds would be wrong here: the intervals last different amounts of time.
Why steepness matters more than height
On the same cumulative-distance graph, a steeper straight section means more distance is covered per second. A point high on the graph means that more distance has already been travelled, not that the pupil is currently faster. In our example, the final point is the highest, but the final section is slower than the section immediately before it.
A horizontal section means the distance reading is unchanged. A curve that becomes steeper indicates increasing speed on a cumulative-distance graph. A straight upward line indicates constant speed, not acceleration. Do not compare the visual angles of two graphs until you have checked their scales: stretching an axis can make the same journey look steeper.
Illustrative AI-generated materials for talking about motion. The image is not a graph or a source of measurement values; use the table for the worked example.
Keep distance, displacement and speed graphs separate
Look at the vertical-axis label again when the next exercise begins. A horizontal line on a speed-time graph describes constant speed, which could be non-zero. A horizontal line on our cumulative-distance graph describes no movement. The shape alone cannot tell you which interpretation applies.
Displacement includes direction from a reference point. Returning towards the start can reduce displacement while the distance travelled continues to grow. A negative gradient on a displacement-time graph can describe motion in the negative direction; it does not mean negative speed. This guide concentrates on distance-time reading, so use your school materials for the further conventions in a displacement question.
The current Cambridge IGCSE Physics 0625 syllabus includes finding speed from the gradient of a straight distance-time section. Our curriculum and assessment guides can help families identify the appropriate course, while physics subject support is the next step for recurring difficulty with motion and calculations.
Use the mistake to choose the next practice task
Give your child a new pair of points: 6 seconds and 12 metres, then 14 seconds and 44 metres. Ask for the speed of the straight section joining them. The answer is 32 divided by 8 = 4 metres per second. If the child divides 44 by 14, practise identifying changes. If the subtraction is right but the unit is missing, focus the next attempt on units rather than repeating the whole explanation.
Bring one attempted question and your child's explanation to a tutoring enquiry. Include the year group, curriculum and topic being studied. For families arranging lessons around a home or villa in Jimbaran, the Jimbaran arrangements page helps frame the location discussion; the exact address and tutor availability still need confirmation. A specific misunderstanding is a better starting point than simply asking for more worksheets.
Frequently asked questions
Does a flat distance-time graph mean constant speed?
For a graph of cumulative distance travelled, a flat section means zero speed during that interval. It is technically constant at zero, but stationary is the clearer description. Do not carry that interpretation over to a flat speed-time graph without reading its vertical value.
Should the graph always start at zero?
The starting point depends on the situation and the chosen reference. Use the values shown. To find the speed of a straight section, calculate the change between two points on that section rather than assuming that it begins at the origin.
Related
Message us on WhatsApp: +62 858 6969 6869 · info@privatetutoringbali.com · We reply within one working day.
Sources and further reading
Published by Private Tutoring Bali. Sources and corrections.