Describe — 2 marks
A cyclist is travelling along a straight road. She accelerates from rest for 5 seconds, reaching a speed of 8 m/s. She then travels at this constant speed for 10 seconds before applying the brakes and decelerating uniformly to a stop over 4 seconds.
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(a) Describe the motion of the cyclist during the first 5 seconds.
[1 mark]
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(b) Describe how the velocity of the cyclist changes during the braking phase.
[1 mark]
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- (a) The cyclist is accelerating / increasing velocity uniformly / at a constant rate from 0 m/s to 8 m/s
- (a) Accept: The cyclist's speed increases / she starts from rest and speeds up
- (b) The velocity decreases uniformly / at a constant rate from 8 m/s to 0 m/s
- (b) Accept: The cyclist decelerates / slows down at a constant rate / velocity changes by the same amount each second
Compare — 5 marks
A cyclist and a runner both travel along the same 100 m straight path. The cyclist accelerates uniformly from rest and reaches 8 m/s after 10 seconds, then maintains this constant velocity. The runner accelerates uniformly from rest and reaches 6 m/s after 12 seconds, then maintains this constant velocity.
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(a) Compare the accelerations of the cyclist and the runner during their acceleration phases.
[2 marks]
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(b) Compare the distances travelled by the cyclist and the runner during their respective acceleration phases.
[2 marks]
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(c) Explain which person travels the 100 m path in less time, using your answers from parts (a) and (b) to justify your response.
[1 mark]
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- (a) Cyclist acceleration = 8 ÷ 10 = 0.8 m/s² (1 mark)
- (a) Runner acceleration = 6 ÷ 12 = 0.5 m/s², so the cyclist has a greater acceleration by 0.3 m/s² (1 mark)
- (b) Cyclist distance during acceleration = ½ × 0.8 × 10² = 40 m (1 mark)
- (b) Runner distance during acceleration = ½ × 0.5 × 12² = 36 m, so the cyclist travels 4 m further during acceleration (1 mark)
- (c) The cyclist reaches constant velocity sooner and has already covered more distance (40 m vs 36 m), so the cyclist completes the 100 m journey in less time / achieves a higher speed allowing them to cover the remaining distance faster (1 mark)
Define — 5 marks
A traffic engineer is analysing the motion of vehicles on a motorway. She needs to understand the difference between how fast a car is travelling at any given instant and how far it travels over a longer journey. The data from speed cameras and GPS tracking systems provides different types of information about vehicle motion.
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(a) Define instantaneous speed.
[2 marks]
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(b) Define average speed and explain how it differs from instantaneous speed.
[2 marks]
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(c) A car travels 240 km in 3 hours, but the speed camera records it travelling at 100 km/h at one point during the journey. Explain why these two pieces of information are not contradictory, using your definitions from parts (a) and (b).
[1 mark]
Show mark scheme
- (a) The speed of an object at a particular / specific moment in time (1 mark)
- (a) Measured over a very small / infinitesimal time interval (1 mark)
- (b) Average speed is the total distance travelled divided by the total time taken (1 mark)
- (b) Instantaneous speed is the speed at one moment, whereas average speed is calculated over a longer time period / journey (1 mark)
- (c) The instantaneous speed (100 km/h) is the speed at one particular moment, but the average speed over 3 hours is 80 km/h (240÷3), so the car must have travelled faster at some points and slower at others during the journey (1 mark)
GCSE Perfect