Distance-Time Graphs (Edexcel GCSE Physics)

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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 1, downloadable IGCSE & GCSE Physics revision notes

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 a 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)

Distance -Time Graph 2, downloadable IGCSE & GCSE Physics revision notes

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 sometimes move 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

Distance -Time Graph 3, downloadable IGCSE & GCSE Physics revision notes

Changing speeds are represented by changing slopes. The red line represents an object slowing down and the green line represents an object speeding up.

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

gradient-distance-time-graph-xy

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.WE Gradient of D-T question graph, downloadable IGCSE & GCSE Physics revision notesCalculate the speed of the train.

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

gradient-of-distance-time-graph-we1

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 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

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:WE Ose gets carried away Question image, downloadable IGCSE & GCSE Physics revision notesa) How long does Ose spend reading his book?There are three sections labelled on the graph: A, B and C.b) Which section represents Ose running home?

c) What is the total distance travelled by Ose?

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

WE Ose gets carried away Ans a, downloadable IGCSE & GCSE Physics revision notes

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:

WE Ose gets carried away Ans c, downloadable IGCSE & GCSE Physics revision notes

Examiner Tip

  • 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!
  • Remember to check the units of variables measured 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.

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Ashika

Author: Ashika

Expertise: Physics Project Lead

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.