Exploring distance time graphs

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# 1,8.5 Distance-time graphs: representing changes in speed

• How can this be shown on the distance-time graph?

First, look at a possible journey in more detail to set up a graphical model of the distance-time relationship. To get started, split the journey into three sections: the journey from Paris to the tunnel, the journey through the tunnel, and the journey from the tunnel to London. An initial assumption is that the train travels at a constant, but different, speed over each section. This simplistic model ignores the details of an actual journey (such as stops at stations and local speed restrictions) to concentrate on the more general features of the distance-time graph.

The first section is from Paris to the tunnel entrance near Calais. This distance is roughly 230 km, so if the train travels at an average speed of 300 km per hour it will take about 230/300 = 0.77 hours, or around 46 minutes. This part of the journey is represented by the distance-time graph in Figure 41.

Figure 41 The Paris-tunnel distance-time graph

Now for the 50 km journey through the tunnel. The train’s average speed drops to about 160 km per hour over this stretch, so the travel time through the tunnel is about 50/160 = 0.31 hours, or just under 20 minutes. This section of the journey begins where the previous section finished-at Calais. So represent it on the distance-time graph as in Figure 42 by drawing another straight line starting where the previous graph ended.

Figure 42 Adding the tunnel section to the distance-time graph

The final stage of the journey is from the tunnel exit near Folkestone to Waterloo in London, a journey of about 100 km. This part of the journey takes about 114 minutes, or 1.9 hours (making a journey time of 180 minutes or 3 hours overall), so the average speed is 100/1.9 = 53 km per hour. Once again, as Figure 43 shows, the distance-time graph is extended by joining on the graph representing this final section.

Figure 43 Adding the final tunnel-London section to the distance-time graph
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