The distance–time relationship — AQA GCSE Physics
Test yourself on The distance–time relationship with AQA GCSE practice questions.
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The distance–time relationship explained
Sketching a distance-time graph from a description is a common task, marked section by section.
Read the full explanation
A stationary period is a horizontal line lasting exactly as long as the description states. Steady motion is represented by a straight line sloping upwards. If the object is accelerating, the line curves upwards with an increasing gradient. Distance is a scalar quantity, meaning the total distance travelled can be plotted regardless of whether the path is straight or curved, though exam questions typically focus on straight-line motion. Always label both axes with the quantity and its unit, use the scale given, and ensure the line is continuous.
The speed of an object can be calculated from the gradient of its distance–time graph.
Speed is distance divided by time, and that is exactly what a gradient is on this graph, so the two are the same calculation. Pick two points far apart on the straight section, because a large triangle reduces the effect of reading error, and take the change in distance together with the change in time between them. A telescope's graph showing 38 km covered in 5.0 s gives a speed of 7.6 km/s. Mark schemes award one mark for reading a correct pair of changes, one for the substitution and one for the answer, so show all three steps. Read the axis units before dividing, because a vertical axis in kilometres and a horizontal axis in seconds give an answer in kilometres per second unless you convert first.
(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.
On a curve the gradient is different at every point, so the speed at one instant is found with a tangent: a straight line that just touches the curve at that time without crossing it. Line a ruler up so that the curve leaves it at the same angle on both sides, draw the tangent long, right across the grid if there is room, and then take the gradient of the ruled tangent rather than of the curve, using two widely separated points on it. Mark schemes award a mark for the tangent drawn at the right time, a mark for attempting the gradient and a mark for the value, and they explicitly refuse a line that cuts through the curve. The steeper the tangent, the faster the object is moving at that instant.
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.
Plotting a distance-time graph from a table requires careful axis setup: time on the horizontal axis and distance on the vertical. Choose scales that fill at least half the grid using sensible increments. Plot each point accurately. For a multi-stage journey, join the points with distinct straight line segments for periods of constant speed, rather than a single line of best fit. A horizontal segment indicates a stationary period. The gradient of any straight section equals the speed. Translating between graphical and numerical forms means calculating speeds from gradients or describing the journey stage by stage, quoting specific times and distances from the axes.
Students should be able to determine speed from a distance–time graph.
Determining a speed from one of these graphs starts with deciding which speed is wanted. The speed during one stage comes from the gradient of that stage alone. The average speed for the whole journey comes from the total distance divided by the total time, which is the gradient of a straight line drawn from the first point to the last, and it is smaller than the fastest stage whenever the object stopped on the way. Comparing two objects drawn on the same axes is quicker still, because the steeper line is the faster one and where the lines cross the two objects are at the same distance at the same time. Take the numbers from the axes rather than counting squares, unless the question states what one square represents.
Your focus
- Sketch a distance-time graph from a written description of a journey.
- Represent a stationary period and a period of constant speed on the same graph.
- Explain why an accelerating object gives a curve of increasing gradient on a distance-time graph.
Show all 15 objectives
- Calculate a speed from the gradient of a straight section of a distance-time graph.
- Select two widely separated points in order to reduce uncertainty in a gradient.
- Convert a gradient read in kilometres per second into metres per second.
- Draw a tangent to a distance-time curve at a stated time.
- Calculate an instantaneous speed from the gradient of that tangent.
- Explain why a chord gives an average speed rather than an instantaneous one.
- Plot a distance-time graph from a table of measurements using connected straight segments for multi-stage journeys.
- Calculate the speed of an object by determining the gradient of a section on a distance-time graph.
- Describe a journey in words from its distance-time graph, quoting values from the axes.
- Determine the speed during a single stage of a journey from a distance-time graph.
- Calculate the average speed for a whole journey shown on such a graph.
- Compare the speeds of two objects plotted on the same distance-time axes.
The distance–time relationship exam tips
Marking Points
- one mark for a horizontal line covering the stationary period and ending at the stated time
- one mark for a straight line with a positive gradient representing constant speed
- one mark for an upward curve of increasing gradient where the object accelerates
- one mark for axes labelled with distance and time, including correct units
- one mark for reading a correct change in distance with the matching change in time
- one mark for a correct substitution into speed = change in distance divided by change in time
- one mark for the correctly calculated speed
- one mark for the unit that follows from the axes, converted where the question requires it
- one mark for a tangent drawn at the stated time that touches the curve without crossing it
- one mark for an attempt to calculate the gradient of the tangent
- one mark for a correct substitution of the change in distance over the change in time
- one mark for the instantaneous speed quoted with its unit
- one mark for time on the horizontal axis and distance on the vertical, both labelled with units
- one mark for sensible scales that use at least half of the available grid
- one mark for all points plotted correctly to within half a small square
- one mark for joining points with distinct straight line segments for multi-stage constant speed journeys
- one mark for a described stage matched to a speed calculated from its gradient
- one mark for identifying whether a stage speed or an average speed is required
- one mark for the gradient of the chosen section calculated from changes read off the axes
- one mark for total distance divided by total time where an average is asked for
- one mark for comparing two lines by their steepness to say which object moves faster
Examiner Tips
- 💡Mark the key times on the axis before drawing the line segments.
- 💡Remember that distance-time graphs never slope downwards; total distance cannot decrease.
- 💡Draw the triangle on the graph itself; examiners give credit for the working shown there.
- 💡Choose points where the line crosses grid lines exactly so the readings are easy.
- 💡Draw the tangent as long as the grid allows and take the two gradient points far apart on it, because a short tangent magnifies reading error.
- 💡Check by eye that the curve pulls away from your ruler symmetrically on both sides.
- 💡Check the scale by counting squares against the largest value before you plot anything.
- 💡Calculate the gradient (change in distance divided by change in time) to find the speed for any straight section.
- 💡Underline average or during this stage in the question before you start.
- 💡Where two lines cross, the objects are level; it is a common single mark.
Common Mistakes
- starting the sloping section at the wrong time because the stationary period was misread
- drawing a downward slope to represent slowing down, which incorrectly implies decreasing total distance
- sketching a straight line where the description says the object accelerates
- dividing a single pair of coordinates rather than using the changes
- using a small triangle, so that reading errors dominate the answer
- taking a gradient across a curved section as though it were straight
- ignoring an axis marked in kilometres or in minutes
- drawing a chord between two points on the curve instead of a tangent
- drawing a line that crosses the curve, which mark schemes do not allow
- taking the gradient of the curve either side of the tangent rather than of the ruled line
- reading the distance at that time and calling it the speed
- drawing a single line of best fit through all points of a multi-stage journey instead of connected segments
- choosing an awkward scale such as three squares to one unit
- plotting time on the vertical axis and distance on the horizontal axis
- describing the graph without quoting any numerical values from the axes
- quoting the speed of the steepest stage as the average speed for the journey
- leaving stationary time out of the total time in an average
- counting squares without checking what one square represents
- giving the distance at a stated time as though it were the speed