Distance-Time Graphs

A distance-time graph is used to describe the motion of an object and calculate its speed

A Distance-Time Graph of an Object Moving Away from the Starting Position

2-1-distance-time-graph

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

Constant Speed on a Distance-Time Graph

Distance-time graphs show the following information:
- If the object is moving at a constant speed
- How fast or slow 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 fast speed
- A shallow slope means the object is moving at a slower speed
- A flat, horizontal line means the object is stationary (not moving)

The Gradient of 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.

Calculating Speed on a Distance-Time Graph

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

$speed = gradient = \frac{∆ y}{∆ x}$

Calculating the Gradient of a Straight Line

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:

$speed = gradient = \frac{∆ y}{∆ x}$

Step 4: Substitute values to calculate the speed

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

$speed = 22.2 m / s$

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

(a)

How long does Ose spend reading his book?

(b)

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

(c)

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 faster 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 (WJEC GCSE Physics: Combined Science)

Revision Note