The graph shows information about part of a cyclist's journey - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 3
Question 23
The graph shows information about part of a cyclist's journey.
Distance travelled (metres)
Work out an estimate of the speed, in m/s, of the cyclist at time 6 seco... show full transcript
Worked Solution & Example Answer:The graph shows information about part of a cyclist's journey - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 3
Step 1
Draw a suitable tangent at t = 6
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Answer
At time 6 seconds, we will draw a tangent line to the curve on the graph. This tangent line will help us estimate the instantaneous speed of the cyclist at that moment.
Step 2
Use a full method to find the gradient of the tangent at t = 6
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Answer
To find the speed, we will select two points on the drawn tangent line. For example, points (5, 10) and (7, 15). The change in distance (Δy) is 15 - 10 = 5 meters, and the change in time (Δx) is 7 - 5 = 2 seconds. Thus, the gradient, which represents speed, can be calculated as:
ext{Speed} = rac{ ext{Change in distance}}{ ext{Change in time}} = rac{5 ext{ m}}{2 ext{ s}} = 2.5 ext{ m/s}
Step 3
Provide the answer
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Answer
The estimated speed of the cyclist at time 6 seconds is approximately 2.5 m/s.
