Exploring distance time graphs

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# 1.8.4 Distance, time and speed: an example

The Eurostar train service that connects London and Paris via the tunnel under the English Channel (la Manche) covers a distance of about 380 km in three hours in 1996. Assuming a constant speed, what would the distance-time graph of this journey look like?

Take the Gare du Nord (the Northern Station) in Paris as the start and measure time and distance from there. The vertical axis on Figure 38 represents distance, in kilometres, from Paris, along the path of the railway track, and the horizontal axis represents the elapsed time, in hours after leaving Paris. The origin of the distance-time graph, the point (0,0), represents the starting point of the journey, and the point (3, 380) represents the arrival of the train at Waterloo Station in London some 380 km away and three hours later. The straight line connecting the points represents the journey from Paris to London, and the gradient of the graph represents the average speed of the journey. In this case, it is 380/3 = 127 km per hour.

Figure 38 Distance-time graph of the Paris-London journey

Figures 39 and 40 show graphically the effect on the journey time of changing the average speed. Increasing the average speed, as in Figure 39, increases the slope of the graph and the journey time is shortened. Reducing the average speed, as in Figure 39, reduces the slope of the graph and lengthens the journey time.

Figure 39 Increasing the average speed
Figure 40 Reducing the average speed

The distance-time graphs in Figures 38, 39 and 40 are based on average speed. But the train does not travel at a constant speed throughout the journey: it will travel faster on some sections of the line than on others.

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