Sheet № 176 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
Question:
A cyclist travels 30 km in 2 hours at a constant speed. What is the speed?
Answer:
2.67 km/h
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?
§Formulas to memorise
Speed = gradient = change in distance ÷ change in time
Average speed = total distance ÷ total time
For each straight section, calculate the gradient: rise (distance) ÷ run (time) = speed.
A horizontal section means speed = 0 (stationary). A downward slope means returning to the start.
Worked example
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
⚠ 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.