Distance-Time Graphs

A picture of a journey

Imagine you could draw a whole journey as a single line. A distance-time graph does exactly that. Instead of writing down "I walked for 10 seconds, stopped, then ran," you draw it — and one glance tells you when the object moved, how fast, and when it rested.

These graphs are one of the most useful tools in physics because motion is often complicated, but a graph makes the story simple to read. If you have met the speed formula in speed, distance and time, this lesson shows you how to see that formula as a shape.

Setting up the axes

Every distance-time graph follows the same rules:

• Time goes along the bottom — the x-axis — usually in seconds.
• Distance goes up the side — the y-axis — usually in metres.

The line always starts at the bottom-left and moves to the right, because time only ever moves forward. The height of the line above the time axis tells you how far the object has travelled from its starting point.

Reading the shape of the line

The beauty of these graphs is that each shape has a clear meaning:

• A flat (horizontal) line → distance is not changing → the object is stationary (resting).
• A straight sloping line → the object moves at a constant speed.
• A steeper line → a faster speed, because more distance is covered in the same time.
• A curved line getting steeper → the object is accelerating (speeding up).
• A curved line getting flatter → the object is decelerating (slowing down).

A line that suddenly drops back down toward zero would mean the object is returning to its starting point.

The key idea: gradient = speed

Here is the most important rule of all. The gradient (the steepness) of a distance-time graph equals the speed. That is because gradient is worked out as:

gradient = change in distance ÷ change in time

and that is exactly the formula for speed (speed = distance ÷ time). So you do not need any new maths — the graph hands you the speed if you read its slope.

Worked examples

Example 1 — constant speed. A line rises steadily from 0 m to 80 m over 16 seconds. What is the speed?

speed = gradient = change in distance ÷ change in time = 80 ÷ 16 = 5 m/s

Example 2 — a journey with a rest. A walker's graph shows three parts:

1. The line rises from 0 m to 30 m in 10 s.
2. The line stays flat at 30 m from 10 s to 25 s.
3. The line rises from 30 m to 90 m between 25 s and 45 s.

What happened, and what was the walker's speed in each moving part?

Part 1: speed = 30 ÷ 10 = 3 m/s (walking). Part 2: flat line, so speed = 0 m/s (the walker stopped for 15 s). Part 3: distance changes by 90 − 30 = 60 m over 45 − 25 = 20 s, so speed = 60 ÷ 20 = 3 m/s.

Reading off the parts one at a time turns a confusing journey into three simple calculations.

Curved lines and changing speed

Real objects rarely move at one steady speed, so many graphs are curved. On a curve, the gradient is different at every point — so the speed is always changing. To find the speed at one particular moment, you draw a tangent: a straight line that just touches the curve at that point, then find the gradient of that line. A curve getting steeper means the object is accelerating, which links directly to ideas in acceleration explained.

Why this matters

Distance-time graphs are not just a school exercise. Engineers use them to plan train timetables, coaches use them to study athletes, and self-driving cars build them constantly to track other vehicles. Learning to read a line as a story of motion is a skill you will use again and again in physics.

Try it yourself! 🧪

Draw your own distance-time graph by walking.

You need a tape measure or a marked path (about 20 m), a stopwatch (a phone works), some chalk or markers, and a friend.

1. Mark a straight line and place markers every 2 metres.
2. Have your friend call out the time every 2 seconds while you walk the path at a steady pace.
3. At each call, note how far along you are. Write down each distance and time as a pair.
4. Back home, plot time on the bottom axis and distance up the side. Join the points.
5. Now repeat, but this time walk, stop for a few seconds, then run. Plot it again.

Compare your two graphs. The steady walk gives a straight slope; the stop-and-run journey gives a flat section followed by a steeper one. You have just turned real motion into a graph — exactly the way scientists do. For the next step, see how the steepness of a speed-time graph reveals acceleration in speed-time graphs.