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A pair of cameras is used on a motorway to help determine the average speed of vehicles travelling between the two cameras - AQA - A-Level Physics - Question 4 - 2020 - Paper 1
Question 4
A pair of cameras is used on a motorway to help determine the average speed of vehicles travelling between the two cameras. Figure 5 shows the speed-time graph for ... show full transcript
Worked Solution & Example Answer:A pair of cameras is used on a motorway to help determine the average speed of vehicles travelling between the two cameras - AQA - A-Level Physics - Question 4 - 2020 - Paper 1
Step 1
Determine whether the average speed of the car exceeded this speed limit.
Answer
To find the average speed of the car, we need to calculate the area under the speed-time graph shown in Figure 5. The total distance travelled by the car can be calculated as follows:
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Calculate the area of the trapezoids in the graph:
Total distance = Area under graph = (1.5 min × 15 m/s) + (1 min × 30 m/s) + (1.5 min × 15 m/s) = 175 m + 1500 m + 225 m = 1850 m.
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Convert the total time into seconds (4 min = 240 seconds):
Average speed = Total distance / Total time = 1850 m / 240 s = 7.71 m/s.
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Since 7.71 m/s is less than the speed limit of 22 m/s, the average speed of the car did not exceed the limit.
Step 2
Step 3
Calculate the time taken for the braking force to stop the car and the distance travelled by the car in this time.
Answer
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Calculate the deceleration using Newton’s second law:
F = ma 6800 N = 1200 kg × a a = 6800 N / 1200 kg = 5.67 m/s².
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Calculate the time taken to stop using the equation:
v = u + at 0 = 31 m/s - 5.67 m/s² × t t = 31 m/s / 5.67 m/s² ≈ 5.47 s.
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Calculate the distance travelled during the braking:
s = ut + 0.5at² = 31 m/s × 5.47 s - 0.5 × 5.67 m/s² × (5.47 s)² ≈ 85 m.
Step 4
Suggest why the chevron separation on motorways does not take into account the distance travelled as a car comes to rest after the brakes are applied.
Answer
The chevron separation does not account for the distance travelled after applying the brakes because it is primarily designed for the driver's response time. The braking distance can vary significantly based on factors such as road conditions, vehicle speed, and the effectiveness of the braking system. Thus, relying solely on reaction time for chevron spacing ensures that drivers maintain a safe distance without considering the potentially variable braking distance.