Distance-Time Graphs (Cambridge (CIE) IGCSE Physics)
Revision Note
Written by: Leander Oates
Reviewed by: Caroline Carroll
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Distance-time graphs
A distance-time graph is used to describe the motion of an object and calculate its speed
Distance-time graph of an object moving at a constant speed
The graph shows a moving object moving further away from its origin at a constant speed
Constant speed on a distance-time graph
If an object is moving at a constant speed, the distance-time graph will be a straight line
If the constant speed is zero, the line will be horizontal
If the constant speed is non-zero, the line will have a gradient
If an object has a speed of zero, the object is stationary
The distance moved by the object over time is zero
The gradient of a distance-time graph represents the magnitude of the object's velocity, or its speed
A steeper slope, or a higher gradient, represents a greater speed
A shallower slope, or a lower gradient, represents a slower speed
Different speeds on a distance-time graph
Both of these objects are moving at a constant speed, because the lines are straight. The steeper slope represents the faster speed and the shallower line represents the slower speed.
Changing speed on a distance-time graph
Often, the speed of an object is not constant
If the speed of an object is changing, the object is accelerating
If an object is accelerating, the distance-time graph will be a curved line
A curve on a distance-time graph is a changing gradient
If the gradient increases over time, the speed is increasing over time
If the gradient decreases over time, the speed is decreasing over time
Speed of an object increasing and decreasing on a distance-time graph
Changing speeds are represented by changing slopes, or gradients. The red line shows a decreasing gradient and represents an object slowing down, or decelerating. The green line shows an increasing gradient and represents an object speeding up, or accelerating.
Using distance-time graphs
The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:
The speed of an object can be found by calculating the gradient of a distance-time graph
is the change in y (distance) values
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.
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
and are labelled, using the units as stated on each axes
Step 2: Convert units for distance and time into standard units
The distance travelled,
The time taken,
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 to calculate the speed
Worked Example
A student decides to take a stroll to the park. They find a bench in a quiet spot, take a seat, and read a book on black holes. After some time reading, the student realises they lost track of time and runs home.
A distance-time graph for the trip is drawn below.
(a) How long does the student spend reading the book?
(b) Which section of the graph represents the student running home?
(c) What is the total distance travelled by the student?
Answer:
Part (a)
The student spends 40 minutes reading his book
The flat section of the line (section B) represents an object which is stationary, so section B represents the student sitting on the bench reading
This section lasts for 40 minutes
Part (b)
Section C represents the student running home
The slope of the line in section C is steeper than the slope in section A
This means the student was moving at a faster speed (running) in section C
Part (c)
The total distance travelled by the student 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
Examiner Tips and Tricks
When calculating a gradient, use the entire line where possible. Examiners tend to award credit if they see a large gradient triangle used, so you need to actually draw the lines directly on the graph itself!
Remember to check the units 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.
You could also be asked to plot a distance time graph from data given to you in a question, or be asked to describe the motion of an object from the data given.
You can read more about the use of graphs in exams in the article Graph skills for GCSE Physics
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