How do you read speed and motion from a distance-time graph?
Distance-time graphs: interpreting the shape of the line, finding speed from the gradient, and using a tangent for the speed of an accelerating object.
A focused answer to Edexcel GCSE Physics 2.7, covering how to interpret distance-time graphs, calculate speed from the gradient, recognise stationary and constant-speed motion, and use a tangent to find the speed of an accelerating object.
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What this dot point is asking
Edexcel statement 2.7 wants you to analyse distance-time graphs, including determining the speed of an object from the gradient of the line, and using a tangent to find the speed of an object that is accelerating.
Reading the shape
The first skill is qualitative: just by looking at the line you can describe the motion. The steeper the line, the greater the speed, because the object covers more distance in the same time. A line that returns towards the time axis would show the object moving back towards its starting point.
Speed from the gradient
For a straight line, pick two points that are far apart to reduce reading error, find the change in distance (the rise) and the change in time (the run), and divide. Using a large triangle rather than two close points makes the gradient much more accurate, which is exactly what examiners reward.
The tangent method for acceleration
When the graph is a curve the speed is changing, so there is no single gradient for the whole line. To find the speed at one moment, draw a tangent that touches the curve at that point, extend it, and find its gradient with a large triangle. This is the only way to read the speed of an accelerating object from a distance-time graph. Drawing the tangent accurately is the skilled part: the tangent should touch the curve at exactly the point of interest and lie along the curve's direction there, neither cutting through it nor leaning to one side.
How Edexcel examines this
Distance-time graphs appear on both tiers, most often as a structured question that first asks you to describe the motion in words and then to calculate a speed from a chosen section. Edexcel mark schemes reward reading a clear, large triangle from the line and showing the change in distance over the change in time as a fraction before dividing, so always write out the two values you read from the axes. A frequent higher-tier twist is a graph with several straight sections of different gradients, where you must identify which section is fastest (the steepest) and calculate its speed, then perhaps describe a flat section as the object being stationary. Take care with the axes: the vertical axis is distance and the horizontal axis is time, so the gradient is distance over time, giving . If a question gives a curved line and asks for the speed at a stated time, that is your signal to draw a tangent rather than join two points on the curve, because joining points on a curve gives an average speed over that interval, not the instantaneous speed asked for.
Try this
Q1. What does a horizontal line on a distance-time graph tell you? [1 mark]
- Cue. The object is stationary (not moving).
Q2. A straight line on a distance-time graph rises over . Calculate the speed. [2 marks]
- Cue. .
Exam-style practice questions
Practice questions written in the style of Pearson Edexcel exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Edexcel 20203 marksA distance-time graph shows a straight line from the origin passing through the point (, ). Calculate the speed of the object, and describe its motion.Show worked answer →
The speed is the gradient: (2 marks). Because the line is straight and sloping, the object moves at a constant (steady) speed (1 mark). Markers reward reading the change in distance and time correctly from the axes and identifying constant speed. Reading single coordinates rather than a change, or using the wrong axis on top, is the usual error.
Edexcel 20224 marksDescribe how to find the speed of an accelerating object at a particular time from a curved distance-time graph, and explain why this method is needed.Show worked answer →
Draw a tangent to the curve at the point in question (1 mark), then find the gradient of that tangent by reading a large change in distance and the corresponding change in time from it and dividing (2 marks). The method is needed because the line is curved, so the gradient (and therefore the speed) is changing, and the tangent gives the instantaneous gradient at that single point (1 mark). Markers reward naming the tangent, using a large triangle for accuracy, and explaining that a curve means a changing speed.
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Sources & how we know this
- Pearson Edexcel GCSE (9-1) Physics (1PH0) specification — Pearson (2016)