Section 1 of 5Reading the Graph
On a distance-time graph the vertical axis shows distance from the starting point and the horizontal axis shows time.
Straight sloping line
- A straight line with a constant gradient shows constant speed, and the steeper the line the greater the speed.
Horizontal line
- A flat line shows the object is stationary, because its distance from the starting point is not changing.
Steep slope
- A steep gradient shows a high speed, since on this type of graph the gradient is equal to the speed.
Curved line
- A curve shows changing speed, and the gradient at any point gives the speed at that instant.
Section 2 of 5Calculating Speed from the Gradient
The gradient is found from a large triangle drawn on a straight section of the graph.
1
Draw a large gradient triangle directly on the straight section, so the working can be checked later.
2
Find Δy as the change in distance and Δx as the change in time, reading both values from the axes.
3
Convert the distance into metres and the time into seconds before dividing, so that the speed is in m/s.
4
Divide the change in distance by the change in time to obtain the speed of the object.
Section 3 of 5Interpreting a Journey
Interpreting a Journey
Total distance
- The final value on the vertical axis gives the total distance travelled from the starting point.
Stopping
- A horizontal section shows the object at rest, and its duration can be read from the time axis.
Comparing speeds
- The section with the steepest gradient is the fastest part of the journey, without any calculation.
Average speed
- Average speed equals total distance divided by total time, so it uses the overall values for the whole journey.
Section 4 of 5Worked Example
Question
- A jogger runs 1.2 km in a straight line at constant speed, taking 8 minutes.
- Calculate the speed of the jogger in m/s.
- Convert the distance1.2 km = 1200 m.
- Convert the time8 minutes = 8 × 60 = 480 s.
- Speed = gradient = change in distance ÷ change in time = 1200 ÷ 480.
- Speed = 2.5 m/s.
Answer The jogger's speed is 2.5 m/s.
Section 5 of 5Exam Checklist & Tips
1.2.1 – Key Points for the Exam
- Distance-time graph A graph that shows how the distance of an object from its starting point changes with time.
- Gradient The change in the vertical value divided by the change in the horizontal value, shown as a slope.
- Speed The distance travelled per unit time, measured in m/s.
- Stationary Not moving, shown by a horizontal line on a distance-time graph.
- Constant speed A speed that does not change, shown by a straight line on a distance-time graph.
Common Mistakes
- Forgetting to convert kilometres and minutes into metres and seconds before calculating the speed.
- Stating that a horizontal line means the object is moving slowly; a horizontal line means it is stationary.
- Using the height of the graph at a point as the speed, instead of the gradient.
- Reading the total distance from the time axis instead of the distance axis.