Distance-Time Graphs

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A distance-time graph shows how the distance of an object moving in a straight line (from a starting position) varies over time:

Distance-time graph

Distance -Time Graph 1, downloadable IGCSE & GCSE Physics revision notes

This graph shows a moving object moving further away from its origin

Constant Speed on a Distance-Time Graph

Distance-time graphs also show the following information:
- If the object is moving at a constant speed
- How large or small the speed is

A straight line represents constant speed
The slope of the straight line represents the magnitude of the speed:
- A very steep slope means the object is moving at a large speed
- A shallow slope means the object is moving at a small speed
- A flat, horizontal line means the object is stationary (not moving)

Faster and slower speed on a distance-time graph

Distance -Time Graph 2, downloadable IGCSE & GCSE Physics revision notes

This graph shows how the slope of a line is used to interpret the speed of moving objects. Both of these objects are moving with a constant speed, because the lines are straight.

Changing Speed on a Distance-Time Graph

Objects might be moving at a changing speed
- This is represented by a curve
In this case, the slope of the line will be changing
- If the slope is increasing, the speed is increasing (accelerating)
- If the slope is decreasing, the speed is decreasing (decelerating)
The image below shows two different objects moving with changing speeds

Acceleration and deceleration on a distance-time graph

Distance -Time Graph 3, downloadable IGCSE & GCSE Physics revision notes

Changing speeds are represented by changing slopes. The red line represents an object slowing down and the green line represents an object speeding up.

Using Distance-Time Graphs

The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:

$speed = gradient = \frac{∆ y}{∆ x}$

Gradient of a distance-time graph

gradient-distance-time-graph-xy

The speed of an object can be found by calculating the gradient of a distance-time graph

$∆ y$ is the change in y (distance) values
$∆ x$ is the change in x (time) values

Worked example

A distance-time graph is drawn below for part of a train journey. The train is travelling at a constant speed. WE Gradient of D-T question graph, downloadable IGCSE & GCSE Physics revision notes

Calculate the speed of the train.

Answer:

Step 1: Draw a large gradient triangle on the graph

The image below shows a large gradient triangle drawn with dashed lines
$∆ y$ and $∆ x$ are labelled, using the units as stated on each axes

gradient-of-distance-time-graph-we1

Step 2: Convert units for distance and time into standard units

The distance travelled = 8 km = 8000 m
The time taken = 6 mins = 360 s

Step 3: State that speed is equal to the gradient of a distance-time graph

The gradient of a distance-time graph is equal to the speed of a moving object:

Step 4: Substitute values in to calculate the speed

$speed = gradient = \frac{∆ y}{∆ x}$

$speed = \frac{8000}{360}$

$speed = 22.2 m / s$

Worked example

Ose decides to take a stroll to the park. He finds a bench in a quiet spot and takes a seat, picking up where he left off reading his book on Black Holes. After some time reading, Ose realises he lost track of time and runs home.

A distance-time graph for his trip is drawn below.

WE Ose gets carried away Question image, downloadable IGCSE & GCSE Physics revision notes

How long does Ose spend reading his book?

There are three sections labelled on the graph, A, B and C. Which section represents Ose running home?

What is the total distance travelled by Ose?

Answer:

Part (a)

Ose spends 40 minutes reading his book
The flat section of the line (section B) represents an object which is stationary - so section B represents Ose sitting on the bench reading
This section lasts for 40 minutes - as shown in the graph below

WE Ose gets carried away Ans a, downloadable IGCSE & GCSE Physics revision notes

Part (b)

Section C represents Ose running home
The slope of the line in section C is steeper than the slope in section A
This means Ose was moving with a larger speed (running) in section C

Part (c)

The total distance travelled by Ose is 0.6 km
The total distance travelled by an object is given by the final point on the line - in this case, the line ends at 0.6 km on the distance axis. This is shown in the image below:

WE Ose gets carried away Ans c, downloadable IGCSE & GCSE Physics revision notes

Examiner Tip

Use the entire line, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used - so remember to draw these directly on the graph itself!

Remember to check the units of variables measured on each axis. These may not always be in standard units - in our example, the unit of distance was km and the unit of time was minutes. Double-check which units to use in your answer.

Distance-Time Graphs (Cambridge O Level Physics)

Revision Note