Draw distance–time graphs from measurements and extract and interpret lines and slopes of distance–time graphs, translating information between graphical and numerical form.
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GCSE Physics Revision
Learn it. Recall it. Revise it.
GCSE Physics revision
The distance–time relationship
Describing motion along a line
Your specification
AQA student objectives
Learning pathway
All · Most · Some
Interpret results or representations related to the distance–time relationship.
Analyse an unfamiliar problem involving the distance–time relationship and justify the method or conclusion.
Revision summary
Key knowledge
Read on screen, then print for Cornell-style active revision.
What is a Velocity-Time Graph?
- A velocity-time graph shows how an object's velocity changes over time, with velocity on the y-axis and time on the x-axis.
- Velocity-time graphs look similar to distance-time graphs, so always double-check which type of graph you are reading in an exam.
Gradient and Acceleration
- The gradient of a velocity-time graph equals the change in velocity divided by the change in time, which is the formula for acceleration: KaTeX parse error: Unexpected character: ' ' at position 5: a =
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- A constant positive gradient indicates constant acceleration, whilst a constant negative gradient indicates constant deceleration.
- A steepening curve means the gradient is increasing, so the rate of acceleration is also increasing.
Calculating Acceleration from the Graph
- To calculate acceleration, substitute the change in velocity and change in time from the relevant section of the graph into KaTeX parse error: Unexpected character: ' ' at position 5: a =
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- For example, if the velocity changes by 3 m/s over 2 seconds, the acceleration is KaTeX parse error: Unexpected character: ' ' at position 1:
Flat Sections: Constant Velocity
- A flat (horizontal) section of a velocity-time graph has a gradient of zero, meaning the object is not accelerating and its velocity is constant.
- To find the constant velocity during a flat section, simply read the value directly from the y-axis.
Finding Distance: Area Under the Graph
- The distance travelled by an object is found by calculating the area under the velocity time graph.
- Regular areas can be split into simple shapes such as triangles and rectangles to make calculation easier.
- The area of a triangle is calculated using 12 × base × height, and the area of a rectangle is base × height.
- Even though area is normally measured in m², the area under a velocity-time graph gives distance travelled in metres (m).
Worked Example: Combining Shapes
- To find the distance in the first 4 seconds, split the area into a triangle (
- 0.5 × 2 × 3 = 3 m) and a rectangle (2 × 3 = 6 m).
- Adding the two areas gives a total distance of 3 + 6 = 9 m for the first 4 seconds.
Estimating Area Under a Curved Section
- When the graph has a curved section, estimate the area by counting the squares on the grid provided as the graph background.
- Partially filled squares should be combined with other partial squares to approximate whole squares before counting.
- For example, if each grid square represents 1 m of distance and you count approximately 8 squares, the estimated distance travelled is around 8 m.
Plotting a Distance-Time Graph
- Each data point is plotted by reading the time and corresponding distance travelled, then marking it on the grid.
- Choose a scale that uses most of the grid to make the graph easier to read accurately.
- Plot each reading as a point, then connect the points to reveal the shape of the motion.
Interpreting the Shape of the Line
- A straight, sloping line means the object is moving at a steady (constant) speed.
- A steeper straight line means a faster speed, because more metres are covered every second.
- A flat (horizontal) line means the object is stationary — the clock keeps running but the distance does not change.
- A curved line means the speed is changing (the object is accelerating or decelerating).
Why the Line Can Never Go Downwards
- Distance travelled is a cumulative total, so it can only increase or stay the same — it can never decrease.
- Even if an object reverses direction, distance already travelled cannot be 'untravelled', so the line stays flat or rises.
- A flat section on a distance-time graph always means the object is stopped, not reversing.
The Gradient of a Distance-Time Graph
- The gradient of a line is calculated by dividing the rise (change in distance) by the run (change in time): gradient = Δ s / Δ t The gradient of a distance-time graph gives the speed of the object, because speed = distance ÷ time, which is the same calculation.
- To measure the gradient, draw a large right-angled triangle directly on the line with its corners on grid lines for accuracy.
- Using a large triangle reduces reading errors, as any small inaccuracy is spread over a bigger change.
Calculating Speed from the Gradient
- Always use the change in distance and the change in time (not the raw end values) when calculating the gradient: speed = Δ s / Δ t For example, if a robot travels from 0 m to 24 m in 30 seconds, its speed is 24 / 30 = 0.8 m/s.
- When a line does not start at the origin, use the coordinates of the two chosen points: e.g.
- 1100 - 300 / 60 - 20 = 800 / 40 = 20 m/s.
- Using the end distance divided by the end time only works if the line passes through the origin — off the origin, it gives the wrong answer.
Comparing Speeds on the Same Graph
- When two objects are plotted on the same axes, the steeper line represents the faster speed.
- You can confirm this by drawing triangles over the same time interval for each line and comparing the distances covered.
- For example, if cyclist A covers 120 m and cyclist B covers 80 m in 20 seconds, their speeds are 6 m/s and 4 m/s respectively.
Common Exam Mistakes to Avoid
- Simply describing the shape of the line (e.g. 'the distance increases with time') does not answer a question asking what the gradient represents — always name the quantity: speed.
- Only about 10% of students correctly recall that the gradient of a distance-time graph represents speed, so learning this key fact is essential.
- Always write down both changes with their units before dividing, as examiners award marks for clear working.
- The answer to 'what does the gradient represent?' is always: 'On a distance-time graph, the gradient is the speed.'.
Worked Example: Train Not Starting at the Origin
- A train's line begins at 20 s and 300 m, and ends at 60 s and 1,100 m — neither corner is at zero.
- The change in distance is 1100 - 300 = 800 m and the change in time is 60 - 20 = 40 s.
- Dividing gives 800 / 40 = 20 m/s, which is the correct speed over that section of the journey.
- Dividing the end distance by the end time (1100 / 60 approx 18.3 m/s) gives an incorrect average that includes time before this section began.
Key Vocabulary Summary
- Gradient: how steep a line is, calculated as rise divided by run, i.e. change in distance divided by change in time.
- Speed: the distance travelled per unit time, measured in metres per second (m/s) at GCSE level.
- Stationary: an object that is not moving; shown as a horizontal (flat) line on a distance-time graph.
- Tangent: a straight line drawn touching a curve at one point, used to find the speed at an instant on a curved distance-time graph (covered at higher tier).
- Distance (S): the total length of the path travelled from the starting point, always measured in metres at GCSE.