4. How far does a bicycle travelling at 1.5 m/s travel in 15 s? 5. A person walks at 0.5 m/s and travels a distance of 1500 m. How long does this take?
USING GRAPHS TO STUDY MOTION Journeys can be summarised using graphs. The simplest type is a distance–time graph, where the distance travelled is plotted against the time of the journey. At the beginning of any measurement of motion, time is usually given as 0 s and the position of the object as 0 m. If the object is not moving, time increases but distance does not. This gives a horizontal line. If the object is travelling at a steady speed, then both time and distance increase steadily, which gives a straight line. If the speed is varying, then the line will not be straight. You can calculate the speed of the object by finding the gradient of the line on a distance–time graph. In Fig. 1.9, which shows a bicycle journey, the graph slopes when the bicycle is moving. The slope gets steeper when the bicycle goes faster. The slope is straight (has a constant gradient) when the bicycle’s speed is constant. The cyclist falls off at about 142 metres from the start. After this, the graph is horizontal because the bicycle is not moving. 160 140
distance/m
120 100 80 60 40 20 0
10
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graph curves as bicycle speed increases
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40
50
time/s straight line as bicycle speed is constant
60 bicycle stops suddenly
70
80 bicycle not moving
Δ Fig. 1.9 A distance–time graph for a bicycle journey.
QUESTIONS 1. How can you tell from a distance–time graph whether the object was moving away from you or toward you?
2. Very often we use sketch graphs to illustrate motion. Describe
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3. Sketch a distance–time graph for a bicycle travelling downhill.
MOTION
the main differences between a sketch graph and a graph.