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The graph shows the speed of a car, in metres per second, during the first 20 seconds of a journey - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 3
Question 16
The graph shows the speed of a car, in metres per second, during the first 20 seconds of a journey. (a) Work out an estimate for the distance the car travelled in t... show full transcript
Worked Solution & Example Answer:The graph shows the speed of a car, in metres per second, during the first 20 seconds of a journey - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 3
Step 1
Work out an estimate for the distance the car travelled in the first 20 seconds. Use 4 strips of equal width.
Answer
To estimate the distance travelled by the car, we'll divide the total time interval (0 to 20 seconds) into 4 equal strips. Each strip will represent a time interval of 5 seconds.
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Calculate the width of each strip:
- Width = Total Time / Number of Strips = 20 s / 4 = 5 s
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Determine the heights (speeds) at the left end of each strip:
- At 0s: Speed = 0 m/s
- At 5s: Speed ≈ 10 m/s
- At 10s: Speed ≈ 20 m/s
- At 15s: Speed ≈ 30 m/s
- At 20s: Speed ≈ 35 m/s
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Calculate the area of rectangles for these strips:
- Strip 1 (0 to 5s): Area = 5s * 0m/s = 0m
- Strip 2 (5 to 10s): Area = 5s * 10m/s = 50m
- Strip 3 (10 to 15s): Area = 5s * 20m/s = 100m
- Strip 4 (15 to 20s): Area = 5s * 30m/s = 150m
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Total estimated distance travelled = 0m + 50m + 100m + 150m = 300m
Step 2
Is your answer to part (a) an underestimate or an overestimate of the actual distance the car travelled in the first 20 seconds? Give a reason for your answer.
Answer
The answer to part (a) is an underestimate of the actual distance travelled. This is because the calculation only considers the speeds at the left ends of the strips and does not account for the higher speeds reached at the right end of each strip. Since the graph is increasing, the actual distance covered by the car during each interval is greater than the areas calculated for each strip. Thus, the area under the curve (actual distance) is greater than the sum of the areas of the rectangles (estimated distance), leading to an underestimate.