Distance-Time Graphs (Cambridge (CIE) IGCSE Physics): Revision Note

You could be asked to describe the motion of an object from data given in a question. You can read more about the use of graphs in exams in the article Graph skills for GCSE Physics

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.

 [4]

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 axis [1 mark]

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

• The distance travelled, $s=8\mathrm{km}=8\times 1000=8000\mathrm{m}$ 

• The time taken, $t=6\min =6\times 60=360\mathrm{s}$ [1 mark]

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:

$\mathrm{gradient}=v=\frac{∆y}{∆x}=\frac{s}{t}$ [1 mark]

Step 4: Substitute values to calculate the speed

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

$v=22.2\mathrm{m}/\mathrm{s}$ [1 mark]

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? [1]

(b) Which section of the graph represents the student running home? [1]

(c) What is the total distance travelled by the student? [2]

Answer:

Part (a)

• The student spends 40 minutes reading their 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 [1 mark]

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 [1 mark]

Part (c)

• The student initially travels a distance of 0.3 km in section A [1 mark]

• The student will run another 0.3 km to return home in section C

• Therefore, the total distance travelled by the student is 0.6 km [1 mark]

Draw the largest gradient triangle possible within the straight section the question asks about. Examiners award credit for seeing the triangle drawn on the graph itself. Do not use the whole line if the graph has more than one section.

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.