Distance-Time Graphs
Simple Explanation
A distance-time graph plots how far an object has travelled against time. The steepness (slope) of the line at any point tells you the object's speed at that point — a steeper line means faster motion, a flat (horizontal) line means the object is stationary.
Why Do We Need It?
Reading a distance-time graph lets you work out an object's speed and describe its whole journey — speeding up, slowing down, stopping — just by looking at its shape.
See It
A distance-time graph with two draggable points and a live speed readout equal to the slope of the line between them
Worked Example
Find speed from a distance-time graph
A distance-time graph shows an object moving from (0 s, 0 m) to (5 s, 20 m) in a straight line. Find its speed.
Why Does This Work?
Slope, by definition, is 'change in y divided by change in x' — on a distance-time graph that is exactly 'change in distance divided by change in time,' which is the definition of speed.
Real-Life Example
A delivery van's tracking data
A delivery company plots a distance-time graph from GPS data to check whether a van was speeding.
A steeper-than-allowed slope over any section of the graph reveals exactly when and where the van exceeded the speed limit.
Practice
A distance-time graph shows a straight line from (0 s, 0 m) to (10 s, 30 m). What is the speed?
MediumCommon mistake
Assuming a curved distance-time graph means the object stopped — a curve actually means the speed is changing, not that motion has stopped; only a completely flat, horizontal line means stationary.
Quick Review
- The slope of a distance-time graph equals speed.
- A steeper line means a faster speed.
- A flat (horizontal) line means the object is stationary.