Here is a speed-time graph. Speed (m/s) 6 | | 5 | * | * 4 | * | * 3 | * | * 2 | * | * 1 |* +-------------------- 0 1 2 3 4 5 6 7 8 9 10 Time (s) (a) Work out an estimate of the gradient of the graph at t = 2 (b) What does the area under the graph represent?

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Here is a speed-time graph - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 1

Question 15

Here is a speed-time graph. Speed (m/s) 6 | | 5 | * | * 4 | * ... show full transcript

Worked Solution & Example Answer:Here is a speed-time graph - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 1

Step 1

Work out an estimate of the gradient of the graph at t = 2

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Answer

To estimate the gradient of the graph at t = 2, we can draw a tangent line at that point on the curve. We note two points on this tangent line. For instance, if we select the point (2, 4) and another point (4, 5), we calculate the gradient using the formula:

$m = \frac{\text{change in speed}}{\text{change in time}} = \frac{5 - 4}{4 - 2} = \frac{1}{2} = 0.5$

Alternatively, using points near this tangent, a rough estimation can suggest a gradient around 0.9.

Step 2

What does the area under the graph represent?

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Answer

The area under the speed-time graph represents the total distance traveled. This is because distance can be calculated by multiplying speed by time, and the area corresponds to this product over the interval of interest.

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