Distance–Time Graphs –

Distance-time graphs are a visual way of representing journeys. They appear frequently on GCSE papers and test your ability to read information from a graph and calculate speeds. The key idea is that the gradient (steepness) of the line represents speed.

What Is a Distance–Time Graph?

A distance-time (DT) graph plots distance on the vertical axis against time on the horizontal axis. Each section of the graph represents a different phase of a journey — travelling, stopping, or returning.

A straight line on a DT graph means constant speed. A steeper line means a faster speed. A horizontal line means the object is stationary (not moving). A line going back down towards zero means the object is returning to the starting point.

At Higher tier, a curved line on a DT graph indicates changing speed (acceleration or deceleration). The speed at any instant can be found by drawing a tangent to the curve at that point and calculating its gradient.

DT graphs are different from speed-time graphs — be sure you know which type you are looking at before answering.

Key Formulas

Step-by-Step Method

1. Read the axes carefully — identify the units for distance and time.
2. For each straight section, calculate the gradient: rise (distance) ÷ run (time) = speed.
3. A horizontal section means speed = 0 (stationary). A downward slope means returning to the start.

Worked Example 1 — Foundation Level

Question: A cyclist travels 30 km in 2 hours at a constant speed. What is the speed?

Working: Speed = distance ÷ time Speed = 30 ÷ 2 Speed = 15

Answer: 15 km/h

Worked Example 2 — Higher Level

Question: A DT graph shows a person walking 4 km in 1 hour, resting for 30 minutes, then walking a further 2 km in 45 minutes. Calculate the average speed for the whole journey.

Working: Total distance = 4 + 2 = 6 km Total time = 1 hour + 0.5 hours + 0.75 hours = 2.25 hours Average speed = 6 ÷ 2.25 = 2.67 (2 d.p.)

Answer: 2.67 km/h

Worked Example 3 — Exam Style

Question: A car travels 60 km in the first hour, then stops for 30 minutes, then returns to the start in 1.5 hours. What is the speed during the return journey?

Working: During the return: distance = 60 km, time = 1.5 hours Speed = 60 ÷ 1.5 = 40

Answer: 40 km/h

Common Mistakes

• Confusing distance-time with speed-time graphs. On a DT graph the gradient is speed. On a speed-time graph the gradient is acceleration and the area under the graph is distance — do not mix these up.
• Including rest time in speed calculations. Speed for a specific section uses only the time and distance for that section, not the whole journey — unless the question asks for average speed.
• Reading the scales incorrectly. Check the intervals on both axes carefully. A grid square might represent 10 minutes, not 1 minute.
• Forgetting that a downward line means returning. A decrease in distance means the object is going back towards the start, not that negative distance exists.

Exam Tips

• Always state the units in your answer — km/h, m/s, mph, etc.
• For average speed, use total distance divided by total time (including rest stops).
• If asked about a specific section, only use the distance and time for that section.
• At Higher tier, draw a tangent to a curve and find its gradient to estimate instantaneous speed.
• When comparing two journeys on the same DT graph, the steeper line represents the faster journey.
• If asked "how long was the person stationary?", read off the length of the horizontal section on the time axis.

Practice Questions

Q1 (Foundation): A walker covers 8 km in 2 hours at a constant speed. What is the gradient of the DT graph?

Q2 (Foundation): A bus travels 45 km in 1.5 hours, then stops for 30 minutes. What is the average speed for the whole journey so far?

Q3 (Higher): On a DT graph a car travels 100 km in 80 minutes, rests for 20 minutes, then returns 60 km in 40 minutes. What is the speed during the return section in km/h?

Practise distance-time graph questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Speed, Distance and Time
• Compound Measures – Density and Pressure
• Other Graphs – Cubic, Reciprocal, Exponential

Summary

• A distance-time graph plots distance (y-axis) against time (x-axis).
• The gradient of the line equals the speed.
• A horizontal line means the object is stationary.
• A steeper line means a faster speed; a downward slope means returning.
• Average speed = total distance ÷ total time.
• At Higher tier, draw tangents to curves to find instantaneous speed.
• Always read the axis scales carefully and convert time units if needed (e.g., minutes to hours).