GCSEScienceAQACombined Science: TrilogyPhysicsRevision NotesForcesDescribing MotionDistance-Time Graphs

Distance-Time Graphs (AQA GCSE Combined Science: Trilogy: Physics): Revision Note

Exam code: 8464

Ashika

Written by: Ashika

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AQA Combined Science: Trilogy: PhysicsAQA Physics

Interpreting Distance-Time Graphs

  • A distance-time graph shows how the distance of an object moving in a straight line (from a starting position) varies over time:

Distance-time graph showing an object moving at constant speed away from its starting position — a straight line with a positive slope
This graph shows a moving object moving further away from its origin

Constant Speed on a Distance-Time Graph

  • Distance-time graphs also show the following information:

    • If the object is moving at constant speed

    • How large or small 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 large speed

    • A shallow slope means the object is moving at a small speed

    • A flat, horizontal line means the object is stationary (not moving)

Two distance-time graphs with straight lines: one with a steep slope representing a large speed, and one with a shallow slope representing a small speed; both objects move at constant speed
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

Two curved distance-time graphs: the red line has a decreasing slope representing a decelerating object; the green line has an increasing slope representing an accelerating object
Changing speeds are represented by changing slopes. The red line represents an object slowing down and the green line represents an object speeding up.

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:

Distance-time graph for Ose's journey, showing three sections labelled A, B and C: A is a straight line going up (walking to park), B is a flat horizontal line (sitting reading), and C is a steeper straight line going up then returning to zero (running home)

a) How long does Ose spend reading his book?

b) Which of the labelled sections (A, B or C) 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

The same distance-time graph with section B highlighted, showing Ose was stationary for 40 minutes

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 larger 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:

The same distance-time graph with the final distance value of 0.6 km marked on the distance axis

Examiner Tips and Tricks

Remember to check the units of variables measured on each axes. 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.

Gradient of 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 space equals space gradient space equals space fraction numerator increment y over denominator increment x end fraction

Distance-time graph showing how to calculate gradient: a right-angled triangle is drawn on the line with the vertical side labelled Δy (change in distance) and the horizontal side labelled Δx (change in time)
The speed of an object can be found by calculating the gradient of a distance-time graph

  • increment y is the change in y (distance) values

  • increment 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.

Distance-time graph for a train journey showing a straight line, used to calculate the train's constant speed from the gradient

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

  • increment y and increment x are labelled, using the units as stated on each axis

The train distance-time graph with a large gradient triangle drawn using dashed lines, with Δy labelled as 8 km and Δx labelled as 6 minutes

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 space equals space gradient space equals space fraction numerator increment y over denominator increment x end fraction

Step 4: Substitute values in to calculate the speed

speed space equals fraction numerator space 8000 over denominator 360 end fraction

speed space equals space 22.2 space straight m divided by straight s

Examiner Tips and Tricks

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!

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Ashika

Author: Ashika

Expertise: Physics Content Creator

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.