Distance-Time Graphs (Oxford AQA IGCSE Combined Science Double Award)

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

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:

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.