What Is a Distance-Time Graph?

A distance-time graph is a graph that shows how the distance travelled by an object changes over time.

Instead of simply telling us how far an object travelled, the graph allows us to see how the object moved during its journey.

For example, a distance-time graph can show when an object:

• moves at a constant speed
• moves faster or slower
• stops moving
• changes its speed

Distance-time graphs are useful for studying the motion of cars, runners, cyclists, trains, and many other moving objects.

 

 

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Reading the Axes

Before interpreting any graph, always check the axes.

On a distance-time graph:

• The x-axis (horizontal axis) represents time.
• The y-axis (vertical axis) represents distance.

Time may be measured in seconds, minutes, or hours.

Distance may be measured in metres or kilometres.

For example, a point at (5 s, 20 m) means:

After 5 seconds, the object has travelled 20 metres.

Always check the units shown on the axes before doing any calculations.

The Slope Tells Us the Speed

The most important feature of a distance-time graph is its slope, also called its gradient.

The slope tells us the speed of the object.

A steep line means that a large distance is covered in a short time.

Therefore:

Steeper line = faster speed

A shallow line means that less distance is covered during the same amount of time.

Therefore:

Shallower line = slower speed

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Calculating Speed from a Distance-Time Graph

We can calculate speed by finding the slope of the graph.

The equation is:

\( speed = \frac{change \ in \ distance}{change \ in \ time} \)

This is sometimes written as:

\( speed = \frac{ \Delta d }{ \Delta t } \)

The symbol Δ means change in.

Worked Example

Imagine an object travels from 10 m at 2 seconds to 40 m at 8 seconds.

First, find the change in distance:

40 - 10 = 30m

Next, find the change in time:

8 - 2 = 6s

Now calculate the speed:

\( speed = \frac{30}{6} = 5 \ m/s \)

The object was travelling at 5 m/s during this section of the graph.

Remember

When calculating the slope, we calculate the change in distance and the change in time.

Do not simply divide any distance value by any time value.

Recognising Types of Motion

Different shapes on a distance-time graph represent different types of motion.

Constant Speed

A straight sloping line represents constant speed.

This means that the object travels equal distances during equal amounts of time.

For example:

The object travels 5 metres every second, so its speed remains constant.

The steeper the straight line, the greater the constant speed.

Stationary Motion

A horizontal line means that the object is stationary.

Stationary means not moving.

Time continues to pass, but the distance does not increase. Therefore, the object's speed is:

0 m/s

For example, a car may stop at a traffic light. The time continues to increase, but the car does not travel any additional distance.

Horizontal line = stationary

 

 

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Changing Speed

Sometimes an object's speed does not remain constant.

A curved line on a distance-time graph represents changing speed because the slope of the graph is changing.

Speeding Up

If the curve becomes steeper, the object's speed is increasing.

The object is covering more distance during each unit of time.

Curve getting steeper = speeding up

Slowing Down

If the curve becomes less steep, the object's speed is decreasing.

The object covers less distance during each unit of time.

Curve becoming flatter = slowing down

Describing Motion from a Graph

A distance-time graph can tell the story of an object's journey.

Imagine a graph showing the following journey:

• From 0 – 10 seconds, the object moves at a constant speed.
• From 10 – 15 seconds, the graph is horizontal.
• From 15 – 20 seconds, the graph rises again with a steeper slope.

We could describe the motion as:

The object moves at a constant speed for the first 10 seconds. It remains stationary from 10 to 15 seconds. It then begins moving again at a faster constant speed.

A good scientific description should include evidence from the graph.

For example, instead of simply saying:

The object stopped.

A stronger answer would be:

The object was stationary between 10 s and 15 s because its distance remained constant at 40 m.

Using values from the graph makes the description more precise.

Constructing a Distance-Time Graph

Distance-time graphs can also be created from experimental data.

Suppose a student records the following results:

To construct a distance-time graph:

1. Put time on the x-axis.
2. Put distance on the y-axis.
3. Choose a suitable scale for each axis.
4. Label both axes and include the correct units.
5. Plot each pair of values.
6. Connect the points appropriately.
7. Give the graph a clear title.

In this example, the points would form a straight line because the object travels the same distance every 2 seconds.

Its speed is:

Real-World Connection

Distance-time graphs can be used to study many real situations.

For example, imagine tracking a student walking from school to a bus stop.

The graph might show:

• a shallow straight line while the student walks slowly
• a horizontal section while the student waits at a crossing
• a steeper line when the student starts running
• another horizontal section when the student reaches the bus stop

By looking only at the graph, we can reconstruct what happened during the journey.

Common Mistake: Distance-Time vs Speed-Time Graphs

Be careful not to confuse a distance-time graph with a speed-time graph.

On a distance-time graph:

slope = speed

A horizontal line means the object is stationary.

On a speed-time graph, however, a horizontal line usually means the object is moving at a constant speed.

Always check the labels on the axes before interpreting a graph.

Did You Know?

Modern smartphones and fitness trackers can collect motion data using technologies such as GPS and motion sensors.

Apps can then display this information as graphs, allowing runners and cyclists to analyse different parts of their journey.

The same basic ideas used in classroom distance-time graphs are therefore useful when analysing real motion data.

Key Vocabulary

Distance-time graph – a graph showing how distance changes with time.

Distance – how far an object has travelled.

Time – how long an event or journey takes.

Slope / Gradient – the steepness of a line on a graph.

Speed – the distance travelled per unit of time.

Constant speed – motion where speed does not change.

Stationary – not moving.

Changing speed – motion in which an object's speed increases or decreases.

Key Takeaways

• A distance-time graph shows distance against time.
• Time is placed on the x-axis and distance on the y-axis.
• The slope of a distance-time graph represents speed.
• A steeper slope represents a greater speed.
• A straight sloping line represents constant speed.
• A horizontal line represents a stationary object.
• A curve represents changing speed.
• A curve becoming steeper shows an object speeding up.
• A curve becoming flatter shows an object slowing down.
• Speed can be calculated using: ( speed = \frac{change \ in \ distance}{change \ in \ time} \)
• Good descriptions of motion should use specific evidence and values from the graph.