Distance-time graphs (Edexcel GCSE Maths): Revision Notes
Distance-time graphs
What are distance-time graphs?
A distance-time graph shows how distance changes over time. These graphs are useful for understanding journeys and calculating speeds. The horizontal axis shows time (usually in minutes or hours), whilst the vertical axis shows distance (usually in metres, kilometres, or miles from a starting point).
The shape and features of the graph tell you important information about the movement or journey being described.
Understanding the Axes:
- Horizontal (x-axis): Time (minutes, hours, etc.)
- Vertical (y-axis): Distance from starting point (metres, km, miles)
- The starting point is typically at the origin (0,0)
Key features to look for
Horizontal lines
A horizontal line means there is no movement - the person or object is stationary or resting. During these periods, the distance from the starting point stays the same, so the line is flat.
Gradient (slope)
The gradient of the line tells you the speed:
- Steeper gradient = faster speed
- Gentler gradient = slower speed
- Negative gradient = moving back towards the starting point
Critical Concept: The gradient (slope) is the most important feature for determining speed. Always look at how steep the line is to understand how fast something is moving.
Straight lines vs curved lines
- Straight lines indicate constant speed - the person is travelling at the same speed throughout that section
- Curved lines show changing speed - the person is either speeding up or slowing down
Reading the time scale
Be careful with time scales on distance-time graphs. The horizontal axis might be marked in:
- Minutes - read directly from the scale
- Hours - remember there are 60 minutes in 1 hour
Common Mistake Alert: Always check the time units! If the scale shows 13:00 to 15:00, this represents a 2-hour period (or 120 minutes). Students often forget to convert between hours and minutes when calculating speed.
Calculating speed
You can find speed from a distance-time graph in two ways:
Method 1: Using the gradient
The gradient of any section gives you the speed for that part of the journey.
Method 2: Using the formula
Worked Example: Calculating Speed
Problem: A person travels 150 metres in 30 seconds on a distance-time graph.
Step 1: Identify the values
- Distance = 150 metres
- Time = 30 seconds
Step 2: Apply the formula
Step 3: Check units The speed is 5 metres per second, which matches our distance (metres) and time (seconds) units.
To use this formula:
- Find the total distance travelled in a section
- Find the time taken for that section
- Divide distance by time
Worked example analysis
When answering questions about distance-time graphs, follow these key strategies:
- To find rest periods: Look for horizontal (flat) sections of the graph
- To find the fastest section: Look for the steepest part of the graph
- To calculate average speed: Use the formula over the required section
- Read scales carefully: Make sure you understand whether time is in minutes or hours
Helpful Tip: When identifying the fastest section, don't just look at the highest point on the graph - look for where the line is steepest (most vertical). The steepest gradient indicates the highest speed.
Exam tips
Essential Exam Strategies:
- Always read the axes labels carefully to understand what units are being used
- Look for flat sections when asked about rest periods
- The steepest section of the graph shows where the person was travelling fastest
- When calculating speed, make sure your units match (if distance is in km and time is in hours, speed will be in km/h)
- Show all your working clearly - examiners award marks for method even if the final answer is wrong
Key Points to Remember:
- Horizontal lines = no movement (resting)
- Steeper gradient = faster speed
- Straight lines = constant speed
- Curved lines = changing speed
- Speed formula:
- Always check your units match when calculating
- The gradient tells you everything about the speed