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.

What each line shape means, at a glance

If you remember one table from this lesson, make it this one:

The line looks like	The object is	Why
Flat (horizontal)	Stopped	Time passes but distance does not change
Straight and sloping	Moving at a steady speed	Equal distance covered in every equal slice of time
Steeper	Moving faster	More distance in the same time — the steeper the line, the greater the speed
Shallower	Moving slower	Less distance in the same time
Curving upwards (getting steeper)	Speeding up (accelerating)	The gradient itself is increasing
Curving over (getting flatter)	Slowing down	The gradient is decreasing
Sloping back down to zero	Returning to the start	Distance from the starting point is shrinking
Vertical	Impossible	It would mean moving a real distance in zero time — infinite speed

That last row is worth pausing on, because it is a common exam trap. A distance-time graph can never have a vertical line. A horizontal line means “stopped”; a vertical line would mean the object teleported. If your sketch has one, you have made a mistake.

A curve that gets progressively steeper is the clearest evidence of acceleration you can put on paper: each second the object covers more ground than the second before, so the gradient — and therefore the speed — is rising the whole way.

How to read the scale

Before you read any value off a graph, work out what one small square is worth. Getting this wrong is the single most common source of lost marks.

1. Find two labelled numbers on the axis, for example 0 and 20.
2. Count the small squares between them — say there are 10.
3. Divide: 20 ÷ 10 = 2, so each square is 2 metres.

Do this separately for each axis; the time axis and the distance axis almost never use the same step. Then read a point by counting squares across and up, and multiplying by the value you worked out.

Two habits that save marks: always read from a gridline rather than eyeballing between them, and when finding a gradient, pick two points as far apart as possible so any small reading error matters less.

Distance-time vs speed-time graphs

These two graphs look similar and mean completely different things. The giveaway is always the y-axis label.

	Distance-time graph	Speed-time graph
y-axis (up the side)	Distance, d, in metres	Speed, v, in m/s
x-axis (along the bottom)	Time, t, in seconds	Time, t, in seconds
The gradient gives you	Speed	Acceleration
A flat line means	Stopped	Steady speed (not stopped!)
The area under the line	Nothing useful	Distance travelled

So a horizontal line means opposite things on the two graphs: on a distance-time graph the object is standing still, but on a speed-time graph it is cruising along at a constant speed. Always check the y-axis label first.

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.