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Here is a speed-time graph for a car - Edexcel - GCSE Maths - Question 16 - 2020 - Paper 3
Question 16
Here is a speed-time graph for a car. (a) Work out an estimate for the distance the car travelled in the first 30 seconds. (b) Is your answer to part (a) an undere... show full transcript
Worked Solution & Example Answer:Here is a speed-time graph for a car - Edexcel - GCSE Maths - Question 16 - 2020 - Paper 3
Step 1
Work out an estimate for the distance the car travelled in the first 30 seconds.
Answer
To estimate the distance travelled in the first 30 seconds, we can calculate the area under the speed-time graph for the interval from 0 to 30 seconds. Looking at the graph:
- The speed is approximately 12 m/s for the first 30 seconds.
- The area can be estimated as a trapezium between 0 seconds and 30 seconds, where the top base is the speed at 0 seconds (0 m/s) and the bottom base is the speed at 30 seconds.
- The average speed can be calculated: Average speed = (0 + 12) / 2 = 6 m/s.
- The distance travelled is then: Distance = Speed × Time = 6 m/s × 30 s = 180 m.
Step 2
Is your answer to part (a) an underestimate or an overestimate of the actual distance the car travelled in the first 30 seconds? Give a reason for your answer.
Answer
The answer to part (a) is likely an overestimate of the actual distance travelled. This is because the graph shows that the speed fluctuates; it starts at 0 m/s and reaches a maximum of around 12 m/s. Since the average speed calculated assumes a constant speed, it does not account for the time spent at lower speeds, which could lead to a more accurate estimation that is lower than 180 m.
Step 3
Work out an estimate for the acceleration of the car at time 60 seconds.
Answer
To estimate the acceleration of the car at time 60 seconds, we can use the formula for acceleration:
ext{acceleration} = rac{ ext{change in speed}}{ ext{change in time}}
From the graph, if we assume the speed is around 13 m/s at 60 seconds and the speed at 0 seconds was 0 m/s:
- Change in speed = Final speed - Initial speed = 13 m/s - 0 m/s = 13 m/s.
- Change in time = 60 seconds.
- Acceleration = .
Step 4
Explain why Julian's method does not give a good estimate of the acceleration at time 60 seconds.
Answer
Julian's method does not give a good estimate of the acceleration at time 60 seconds because he calculated it based on a single point speed from the graph without accounting for the change over time. The acceleration should consider the speed just before 60 seconds and just after (if available). Since the speed at 60 seconds is 13 m/s, a more accurate estimation would need to consider the curve of the graph, which reflects changes in acceleration, rather than a simple subtraction that overlooks the graph's shape and the varying speed.