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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 - Edexcel - GCSE Maths - Question 17 - 2020 - Paper 3
Question 17
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, (a) Work out an estimate for the distance the car travelled in the first 30 seconds - Edexcel - GCSE Maths - Question 17 - 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 by the car in the first 30 seconds, we calculate the area under the speed-time graph from 0 to 30 seconds. The graph indicates a triangular shape for the first half (0 to 15 seconds) and a trapezoid shape for the second half (15 to 30 seconds).
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Calculate the area of the triangle (0 to 15 s):
- Base = 15 s, Height = 12 m/s:
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Calculate the area of the trapezoid (15 to 30 s):
- Height1 = 12 m/s, Height2 = 6 m/s, Base = 15 s:
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Total distance (0 to 30 s):
Thus, an estimate of the distance travelled in the first 30 seconds is approximately 225 meters.
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?
Answer
The estimate obtained in part (a) is an overestimate of the actual distance travelled by the car in the first 30 seconds. This is because the speed-time graph shows that the speed decreases after reaching its peak at around 15 seconds. As a result, the area calculated under the curve for distances represents more distance than actually travelled since it does not account for the reduction in speed after 15 seconds.
Step 3
Work out an estimate for the acceleration of the car at time 60 seconds.
Answer
To determine the acceleration of the car at time 60 seconds, we need to find the speed at that moment. From the speed-time graph, the speed at 60 seconds is estimated to be 6 m/s.
The acceleration formula is:
Given that the speed is 6 m/s at this moment and using the time interval of 60 seconds,
Julian's method using an average speed does not account for variations in speed over the 60 seconds, which can lead to inaccuracies.
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 provide a good estimate of acceleration because it relies on a single average speed measurement to find acceleration at a specific moment (60 seconds) rather than considering the instantaneous speed of the car at that time. The car's speed changes over time, and applying an average speed leads to a significant approximation error, especially considering that the graph shows considerable fluctuation in speed before and after 60 seconds. Thus, the acceleration should ideally be calculated using the actual speed at the specific time, not just the average.