Distance-Time Graphs (Oxford AQA IGCSE Physics)
Revision Note
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 in a straight line
Constant speed on a Distance-Time graph
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
Calculating Speed from a Distance-Time Graph
The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:
Where:
is the change in y (distance) values
is the change in x (time) values
Calculating the gradient of a straight line
The gradient of a distance-time graph is equal to the object's speed
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
The and magnitudes are labelled, using the units as stated on each axes
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 to calculate the speed
Worked Example
A man 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, the man realises he lost track of time and runs home.
A distance-time graph for his trip is drawn below.
(a) How long does the man spend reading his book?
(b) There are three sections labelled on the graph, A, B and C. Which section represents the man running home?
(c) What is the total distance travelled by the man?
Answer:
Part (a)
The man 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 man sitting on the bench reading
This section lasts for 40 minutes - as shown in the graph below
Part (b)
Section C represents the man running home
The slope of the line in section C is steeper than the slope in section A
This means the man was moving with a faster speed (running) in section C
Part (c)
The total distance travelled by the man 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:
Examiner Tip
Use the entire line or line segment 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 these examples, the unit of distance was km and the unit of time was minutes. Double-check which units to use in your answer.
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