The distance–time relationship — AQA GCSE Combined Science
Test yourself on The distance–time relationship with AQA GCSE practice questions.
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The distance–time relationship explained
A distance–time graph plots distance travelled on the vertical axis against time on the horizontal axis for motion along a straight line.
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The gradient of the line gives the speed: a steeper line means a greater speed, a horizontal line means the object is stationary, and a straight line means constant speed. For example, a cyclist travelling 100 m in 20 s gives a straight line from (0 s, 0 m) to (20 s, 100 m), with gradient 100 m ÷ 20 s = 5 m/s. A curved line shows changing speed, meaning the object is accelerating or decelerating. The graph represents distance travelled, not displacement, so it does not show direction. Reading values from the axes and calculating gradients for straight lines are key skills.
The speed of an object can be calculated from the gradient of its distance–time graph.
A distance–time graph plots distance travelled on the vertical axis against time on the horizontal axis. For an object moving at constant speed, the line is straight and its gradient equals the speed. Gradient means vertical change divided by horizontal change, so choose two points on the line that are far apart, read the distance values and the time values, subtract to find each change, then divide distance change by time change. For example, if distance rises from 20 m to 80 m between 4 s and 16 s, the gradient is (80 − 20) ÷ (16 − 4) = 60 ÷ 12 = 5 m/s. A steeper line means a greater speed; a horizontal line means the object is stationary. Units come from dividing metres by seconds, giving m/s.
(HT only) If an object is accelerating, its speed at any particular time can be determined by drawing a tangent and measuring the gradient of the distance–time graph at that time.
This is a Higher Tier only skill. When an object accelerates, its distance–time graph is curved, so the gradient changes continuously and no single straight-line gradient gives the speed throughout. The speed at one instant equals the gradient of the tangent at that point. Draw a straight line that touches the curve at the chosen time and continues equally on both sides, then choose two well-separated points on that tangent, read their coordinates, and divide the change in distance by the change in time. For example, a tangent at 3 s might pass through 10 m at 1 s and 50 m at 5 s, giving (50 − 10) ÷ (5 − 1) = 40 ÷ 4 = 10 m/s. A steeper tangent means a higher instantaneous speed.
Students should be able to draw distance–time graphs from measurements and extract and interpret lines and slopes of distance–time graphs, translating information between graphical and numerical form.
Distance–time graphs show how far an object has travelled from a start point over time. To draw one, record distance at regular times, choose scales, plot points, then join them with straight lines or smooth curves. The slope (gradient) tells you speed: a steeper line means faster motion, a horizontal line means stationary, and a straight line means constant speed. You must also translate between graph and numbers: read distance and time values from axes, calculate speed as distance ÷ time, and use the gradient to describe motion. For example, if a cyclist travels 100 m in 20 s, the gradient is 100 m ÷ 20 s = 5 m/s. Interpreting lines includes identifying acceleration (curve getting steeper), deceleration (curve getting shallower), and rest (flat line). Always label axes with quantity and unit, and use a ruler for straight lines.
Students should be able to determine speed from a distance–time graph.
Speed is found from a distance–time graph by calculating the gradient. For a straight line, pick two points, read the change in distance (Δd) and time (Δt), then divide: speed = Δd ÷ Δt. For example, if distance changes from 20 m to 80 m while time changes from 4 s to 16 s, Δd = 60 m and Δt = 12 s, so speed = 60 m ÷ 12 s = 5 m/s. If the line is curved, speed is changing; find average speed using total distance and total time. Higher Tier students must also estimate instantaneous speed by drawing a tangent and finding its gradient. Always include units (m/s) and show working. A horizontal line gives zero speed. A steeper line means a higher speed. This skill requires reading values from axes, performing the division, and interpreting the result.
Your focus
- Plot and interpret a distance–time graph for motion along a straight line.
- Determine speed from the gradient of a straight-line distance–time graph.
- Distinguish between stationary, constant-speed and changing-speed motion from the shape of the graph.
Show all 15 objectives
- Read coordinates accurately from the axes of a distance–time graph.
- Calculate speed by dividing the change in distance by the change in time.
- Interpret the steepness and shape of a distance–time graph in terms of speed.
- Draw an appropriate tangent to a curved distance–time graph at a specified time (Higher Tier only).
- Calculate the gradient of a tangent to find instantaneous speed.
- Explain why a tangent is needed when speed is changing rather than constant.
- Plot a distance–time graph from a table of measurements using appropriate scales and labels.
- Calculate the gradient of a distance–time graph and state its meaning as speed.
- Describe the motion shown by horizontal, straight sloping and curved sections of a distance–time graph.
- Calculate speed from the gradient of a straight-line section of a distance–time graph.
- Interpret the numerical value of speed in the context of the motion shown on the graph.
- (Higher Tier only) Estimate instantaneous speed from a curved distance–time graph by drawing a tangent.
The distance–time relationship exam tips
Marking Points
- Plots distance travelled on the vertical axis and time on the horizontal axis with suitable scales and labels.
- Interprets the gradient of the line as the speed of the object.
- Identifies a horizontal line as an object at rest and a straight sloping line as constant speed.
- Calculates speed from the gradient using speed = distance ÷ time with correct units.
- Recognises that a curved line represents changing speed, indicating acceleration or deceleration.
- Identify the vertical axis as distance and the horizontal axis as time, and state that gradient means change in distance divided by change in time.
- Select two clearly separated points on the straight line, read their coordinates accurately from the axes, and subtract to find the changes rather than reading single values.
- Divide the change in distance by the change in time, including correct units such as m/s, and interpret a larger gradient as a greater speed.
- Explain that a horizontal section represents zero speed because the distance does not change as time increases, and that a straight line shows constant speed.
- Recognise that a curved distance–time graph shows changing speed, so the gradient must be found at a single point rather than between two points on the curve (Higher Tier only).
- Draw a tangent that touches the curve at the required time and extends on both sides, judging it by eye so it matches the curve's direction at that point.
- Choose two widely spaced points on the tangent, read their coordinates, and calculate change in distance divided by change in time to obtain the instantaneous speed.
- State the answer with correct units such as m/s and relate a steeper tangent to a greater speed at that instant.
- Plot distance on the y-axis and time on the x-axis with sensible scales and labelled units.
- Draw a line or curve of best fit through plotted points, using a ruler for straight sections.
- Calculate gradient as change in distance divided by change in time, including correct units.
- Interpret a horizontal line as stationary, a straight sloping line as constant speed, and a curve as changing speed.
- Translate between graph and numerical form by reading values from axes and substituting into speed = distance ÷ time.
- Describe motion in words using gradient: steeper slope means greater speed, shallower slope means lower speed.
- Select two points on the line and read the corresponding distance and time values accurately from the axes.
- Calculate change in distance (Δd) and change in time (Δt) by subtraction, ensuring correct units.
- Divide Δd by Δt to obtain speed, and state the unit as m/s (or appropriate unit).
- For curved graphs, use total distance and total time for average speed, or (Higher Tier only) use a tangent at a point to estimate instantaneous speed.
- Interpret zero gradient as zero speed and a steeper gradient as a higher speed.
- Show working clearly, including the equation speed = distance ÷ time and substitution of values.
Examiner Tips
- 💡Label both axes with quantity and unit before plotting or reading points.
- 💡Show the gradient calculation clearly, including the values substituted and the unit m/s.
- 💡Check whether the graph is a straight line or a curve before deciding whether speed is constant or changing.
- 💡Draw the two chosen points on the graph and mark the vertical and horizontal changes before calculating, so your method is visible.
- 💡Use points on grid intersections where possible to reduce reading error, and show the subtraction step clearly.
- 💡Check the size of your answer against the graph: a steeper line should give a larger speed than a shallower one.
- 💡Use a ruler and extend the tangent well beyond the curve so two widely separated points can be read accurately.
- 💡Mark the two points on the tangent clearly and show the subtraction and division, since method marks may be available even if the final value is slightly out.
- 💡Sanity-check the value: if the curve is getting steeper, the tangent gradient at a later time should be larger.
- 💡Always label axes with quantity and unit, for example distance / m and time / s, before plotting points.
- 💡When finding speed from a graph, choose two points on the line that are far apart to reduce reading error, then show the subtraction clearly.
- 💡Check the units on both axes and convert if necessary, for example cm to m or minutes to seconds, before calculating speed.
- 💡Choose two points on the line that are far apart and lie exactly on grid lines to make reading values easier and more accurate.
- 💡Write down the equation speed = distance ÷ time before substituting numbers, so your method is clear.
- 💡Check that your answer has the correct unit and a sensible size; for example, a car speed of 500 m/s is unrealistic, so re-check your calculation.
Common Mistakes
- Reading the vertical axis as speed rather than distance: correct this by checking the axis label before interpreting the graph.
- Assuming a horizontal line means the object is moving slowly: correct this by stating it shows the object is stationary.
- Calculating gradient as time ÷ distance: correct this by dividing the change in distance by the change in time.
- Dividing the time change by the distance change: correct this by remembering gradient is rise over run, so distance change goes on top.
- Reading a single coordinate and dividing distance by time without subtracting: correct this by using two points and finding the differences first.
- Forgetting units or writing km/h when the axes use metres and seconds: correct this by deriving units from the axes, giving m/s here.
- Drawing a chord between two points on the curve instead of a tangent: correct this by making the line touch the curve at one point only and follow its direction there.
- Using the point of contact as one of the two calculation points and reading a single coordinate: correct this by selecting two separate points on the tangent and subtracting.
- Drawing a tangent that crosses the curve or sits at the wrong angle: correct this by checking that the tangent and curve have the same slope at the point of contact.
- Plotting time on the y-axis and distance on the x-axis: correct by always putting distance on the y-axis and time on the x-axis.
- Calculating gradient as time ÷ distance instead of distance ÷ time: correct by using gradient = change in y ÷ change in x, which gives speed.
- Joining points with a jagged line rather than a line of best fit: correct by drawing a single straight line or smooth curve that best represents the trend.
- Using the coordinates of a single point instead of the change between two points: correct by always subtracting to find Δd and Δt.
- Forgetting to convert units, for example using minutes on the time axis but seconds in the speed unit: correct by converting all values to consistent units before dividing.
- Assuming the gradient of a curved line is constant: correct by recognising that speed changes and using average speed or (Higher Tier only) a tangent.