A car moves from rest. The graph gives information about the speed, v metres per second, of the car / seconds after it starts to move. (a) (i) Calculate an estimate of the gradient of the graph at t = 15 (ii) Describe what your answer to part (i) represents. (b) Work out an estimate for the distance the car travels in the first 20 seconds of its journey. Use 4 strips of equal width.

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A car moves from rest - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 2

Question 18

A car moves from rest. The graph gives information about the speed, v metres per second, of the car / seconds after it starts to move. (a) (i) Calculate an estimat... show full transcript

Worked Solution & Example Answer:A car moves from rest - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 2

Step 1

Calculate an estimate of the gradient of the graph at t = 15

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Answer

To find the gradient at t = 15 seconds, draw a tangent line at that point on the graph. The gradient is calculated as the change in speed divided by the change in time. From the graph, estimate the change in speed (from 20 m/s to approximately 15 m/s) over the change in time (from 10 seconds to 20 seconds):

$\text{Gradient} = \frac{\text{Change in Speed}}{\text{Change in Time}} = \frac{15 - 20}{15 - 10} = \frac{-5}{5} = -1$

Thus, the estimated gradient is approximately -1 m/s².

Step 2

Describe what your answer to part (i) represents.

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Answer

The gradient at t = 15 seconds represents the rate of change of speed of the car at that specific time. A negative gradient indicates that the car is decelerating at that point in time.

Step 3

Work out an estimate for the distance the car travels in the first 20 seconds of its journey. Use 4 strips of equal width.

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Answer

To estimate the distance traveled over the first 20 seconds, divide the time into 4 equal intervals of 5 seconds each. Use the trapezoidal rule to calculate the area under the speed graph:

Interval 0 to 5 seconds: Speed is approximately 5 m/s. Area = 5 m/s × 5s = 25 m
Interval 5 to 10 seconds: Speed increases to 15 m/s. Average speed = (5 + 15) / 2 = 10 m/s. Area = 10 m/s × 5s = 50 m
Interval 10 to 15 seconds: Speed is 20 m/s. Area = 20 m/s × 5s = 100 m
Interval 15 to 20 seconds: Speed decreases to 15 m/s. Average speed = (20 + 15) / 2 = 17.5 m/s. Area = 17.5 m/s × 5s = 87.5 m

Now, sum the areas:

$\text{Total Distance} = 25 + 50 + 100 + 87.5 = 262.5 \text{ meters}$

Round your answer to an estimate of around 220 meters for simplicity.

A car moves from rest - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 2

Worked Solution & Example Answer:A car moves from rest - Edexcel - GCSE Maths - Question 18 - 2019 - Paper 2

Calculate an estimate of the gradient of the graph at t = 15

Describe what your answer to part (i) represents.

Work out an estimate for the distance the car travels in the first 20 seconds of its journey. Use 4 strips of equal width.

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