Motion graphs: revision notes and practice

What you will learn

• Read units and intervals from distance–time and velocity–time graphs.
• Calculate straight-line gradients and whole-journey averages correctly.
• Interpret stationary motion, constant velocity and, where permitted, graph areas.

Key rules

Distance–time gradient

Speed = change in distance ÷ change in time. A horizontal distance–time line means stationary.

Velocity–time gradient

Average acceleration = change in velocity ÷ time interval. A horizontal line means constant velocity.

Velocity–time area

Signed area gives displacement; add magnitudes of separate areas for distance. Area calculations are omitted from named Foundation courses in this app.

Worked examples

Example 1: Distance rises from 10 m to 34 m between 2 s and 8 s. Find the speed.

1. Change in distance = 34 − 10 = 24 m.
2. Change in time = 8 − 2 = 6 s.
3. Divide 24 by 6.

4 m/s

Example 2: Higher/general practice: velocity rises uniformly from 0 to 6 m/s in 4 s. Find the distance.

1. The velocity–time area is a triangle.
2. Distance = ½ × 4 × 6.

12 m

A practice question

The distance–time graph shows a straight journey from 0 to 7 s. Calculate the speed over this interval.

1. Read the axes before interpreting the line

A motion graph links a quantity to time; it is not a drawing of the route. Check the horizontal axis, vertical axis and units before doing any calculation. A point at 5 seconds and 20 metres means that the recorded distance at that time is 20 metres. It does not say that the object has climbed a twenty-metre hill.

Read the scale carefully. A labelled gap of ten units may contain several smaller divisions, so each division is worth less than ten. Find two labelled values and count the equal gaps between them. Read a value by following from the axis to the plotted line, then across to the other axis. Include the unit stated on that graph.

2. Distance–time gradients describe speed

For a straight section, speed is the change in distance divided by the elapsed time. Use two points on that same section, preferably far apart to reduce the relative effect of small reading errors. If distance changes from 12 metres to 36 metres between 3 seconds and 9 seconds, the speed is (36 − 12)/(9 − 3) = 4 metres per second.

A steeper distance–time line corresponds to a greater speed when the scales are unchanged. A horizontal section has zero gradient: recorded distance stays constant while time passes, so the object is stationary. A straight sloping section represents constant speed. Comparing visual steepness across graphs with different scales is unreliable; calculate the gradients instead.

speed = Δdistance/Δtime; distance in m, time in s, speed in m/s

3. Choose the correct time interval

The difference between two times is not necessarily the later time. For an interval from 4 to 10 seconds, use six seconds. Similarly, if the graph begins away from the origin, subtract the earlier distance from the later distance. Dividing an absolute vertical coordinate by an absolute horizontal coordinate only works in the special case where the chosen section begins at the origin.

For a complete journey, average speed is total distance divided by total elapsed time. Include stops in the elapsed time. Travelling 40 metres in 10 seconds, stopping for 5 seconds, then travelling 20 metres in 5 seconds gives 60 metres in 20 seconds, or 3 metres per second. Simply averaging the speeds of the moving sections ignores their durations and the stop.

4. Velocity–time graphs use a different gradient

Velocity includes direction. A velocity–time graph shows how velocity changes, and its gradient gives acceleration. If forward velocity increases from 2 to 8 metres per second over three seconds, average acceleration is (8 − 2)/3 = 2 metres per second squared. A straight sloping line means constant acceleration over that interval.

A horizontal velocity–time section means constant velocity. When that value is above zero, the object is moving rather than stationary. Negative acceleration means velocity is decreasing in the chosen positive direction; whether the object slows down depends on its velocity direction. The app uses forward motion in these introductory tasks, making decreasing positive velocity a slowing-down case.

average acceleration = Δvelocity/Δtime; acceleration in m/s²

5. Areas connect velocity to displacement

In General and Higher practice, use the area between a velocity–time line and the time axis to find displacement. A constant velocity of 5 metres per second for 4 seconds forms a rectangle with area 5 × 4 = 20 metres. Velocity units multiplied by seconds become metres. The line height itself remains a velocity, not a distance.

A uniform increase from zero to 6 metres per second over 4 seconds forms a triangle. Its area is half the base multiplied by the height: 0.5 × 4 × 6 = 12 metres. Break more complicated straight-line graphs into rectangles and triangles. Named Foundation courses in this app replace area tasks with graph readings or gradient calculations.

6. Distinguish distance from displacement

Displacement describes change in position with a direction; distance measures the length of the route. For a velocity–time graph that stays above the time axis, motion stays in the positive direction and both have the same numerical magnitude. Areas below the time axis contribute negative displacement. For total distance, add the magnitudes of the separate positive and negative areas.

A speed–time graph never uses a negative speed. Its area represents distance. A velocity–time graph can cross the axis when direction changes. A graph described as distance travelled cannot decrease as time increases; a position or displacement graph can. Read the exact axis wording rather than treating distance, position, speed and velocity as interchangeable names.

7. Obtain and evaluate motion data

In a supervised trolley investigation, define a fixed position origin and record positions at known times. A calibrated motion sensor or carefully placed distance markers can provide data. Keep the track straight and clear, follow the teacher’s procedure, and record units. Plot time horizontally, using sensible scales that spread the data across the graph.

Repeat controlled runs and look for consistent patterns rather than hiding readings that disagree. Timing delays can shift recorded times, and imprecise position readings affect calculated gradients. Explain which quantity is uncertain and how that affects the result. Long intervals between two graph points reduce the relative effect of small reading errors, provided both points lie on the same straight section.

8. Explain a graph using evidence

A strong written explanation connects a graph feature to a physical quantity. For a horizontal distance–time segment, say that distance stays constant while time passes, so speed is zero. For a horizontal velocity–time segment above the axis, say that velocity is constant and non-zero, so acceleration is zero while the object continues moving. Simply writing horizontal is not a complete physical interpretation.

Check a numerical result against the whole journey. An average speed including a long stop should be lower than the corresponding moving-only average. A triangular velocity–time area should be half the rectangle with the same base and height. These checks provide evidence for an answer and can reveal a mistaken axis, a missing subtraction or a missing factor of one half.

Check your understanding

How to earn the marks

• Name the axes before choosing gradient or area.
• Subtract both coordinates to obtain the correct changes.
• Include stops in whole-journey averages.
• Keep distance and displacement distinct; use the permitted methods for your selected tier.

A common mistake

A graph is not a picture of the track. A rising distance–time line means changing distance, not climbing a hill.

Course context and official specifications

This guide covers selected skills. Some extensions are Higher content; choose your official tier separately from practice difficulty in the app. These are original questions and explanations.

• AQA GCSE Physics — 4.5.6.1.4–4.5.6.1.5

  Straight-line speed and acceleration gradients are available at Foundation. Area under velocity–time graphs and tangents to accelerating distance–time graphs are Higher-only in this specification.

• Edexcel GCSE Physics — 2.7; 2.10

  Edexcel permits uniform-acceleration velocity–time areas at Foundation (2.10c). This selected Foundation bank focuses on readings and straight-line gradients; it does not cover every permitted graph skill.

• OCR Gateway GCSE Physics A — P2.1e–P2.1f

  Line and slope interpretation is available at Foundation. P2.1f, enclosed velocity–time areas, is Higher-only; Foundation practice uses straight-line gradients and readings.

• OCR Twenty First Century GCSE Physics B — P4.2.8–P4.2.10

  Line and slope interpretation is available at Foundation. P4.2.10, enclosed velocity–time areas, is Higher-only; Foundation tasks use straight-line gradients and graph readings.

Keep your next step small

Try five questions, read the feedback, and revisit one thing you found difficult. The app tracks a 20-answer practice goal separately from accuracy.

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