1.8.12 Distance-time graphs: summing up
A distance-time graph is a graph of distance measured from a specific place and along a particular route, plotted against time measured after a specific time. The gradient on such a graph gives the numerical value of the average speed and indicates the direction of travel. Speed is an unsigned quantity equal to the distance travelled along a set route divided by time irrespective of direction towards or away from the starting point (the origin for distance measurement). A positive gradient indicates travel away from the starting point and a negative gradient indicates travel towards the starting point. Speed and direction together give the velocity of travel, which is represented by the gradient of the graph.
Activity 22: Planning a journey
Use a series of labelled diagrams to show how you would construct and use a distance-time graph for planning a journey. Your audience is a group of people planning a sponsored cycle ride. You do not know them, but you are aware they are not confident with mathematics.
Diagrams are often helpful in making ideas easier to understand. In planning your series of diagrams, you needed to show the particular properties and characteristics of distance-time graphs and how you use them to take readings. As your audience may not have met such graphs before, your diagrams should be clear and labelled appropriately. You may need to limit your use of technical language or explain it. Each diagram could, for instance, demonstrate a particular feature, until the final diagram is a completed graph-perhaps with an example showing how to use it.
Your diagrams should include the following elements developed in a logical order.
A vertical axis and a horizontal axis that are both labelled, including units. The vertical axis should give the distance from a specified place (in a specified direction) at a time shown on the horizontal axis (after a specified time).
The journey points are correctly plotted on the graph, are labelled and joined with straight lines.
A title for the graph.
The example needs to demonstrate that the slope of the graph gives the average speed between two places: the steeper the slope, the faster the average speed. Parts of the graph sloping upwards/downwards mean travel is away from/towards the starting point.