A-Level Edexcel Maths Pure Basic Trigonometry: The speed, v m s⁻¹, of a train a

The speed, v m s⁻¹, of a train at time t seconds is given by v = \\sqrt{(1.2t - 1)}, \\ 0 \leq t \leq 30 - Edexcel - A-Level Maths Pure - Question 8 - 2006 - Paper 2

Question 8

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The speed, v m s⁻¹, of a train at time t seconds is given by v = \\sqrt{(1.2t - 1)}, \\ 0 \leq t \leq 30. The following table shows the speed of the train at 5 sec... show full transcript

Worked Solution & Example Answer:The speed, v m s⁻¹, of a train at time t seconds is given by v = \\sqrt{(1.2t - 1)}, \\ 0 \leq t \leq 30 - Edexcel - A-Level Maths Pure - Question 8 - 2006 - Paper 2

Step 1

Complete the table, giving the values of v to 2 decimal places.

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Answer

To complete the table, we need to calculate the values of v for t = 15, 20, and 25 seconds using the given formula:

For t = 15: $v = \\sqrt{(1.2 \times 15 - 1)} = \\sqrt{(18 - 1)} = \\sqrt{17} \\approx 4.12.$
For t = 20: $v = \\sqrt{(1.2 \times 20 - 1)} = \\sqrt{(24 - 1)} = \\sqrt{23} \\approx 4.79.$
For t = 25: $v = \\sqrt{(1.2 \times 25 - 1)} = \\sqrt{(30 - 1)} = \\sqrt{29} \\approx 5.39.$

The completed table is:

t \ 0 \ 5 \ 10 \ 15 \ 20 \ 25 \ 30 v \ 0 \ 1.22 \ 2.28 \ 4.12 \ 4.79 \ 5.39 \ 6.11.

Step 2

Use the trapezium rule, with all the values from your table, to estimate the value of s.

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Answer

To estimate the distance s travelled by the train, we use the trapezium rule with the values calculated earlier:

The formula for the trapezium rule is: $s \approx \frac{h}{2} \left( f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + 2f(x_4) + f(x_n) \right)$ where h is the interval (5 seconds) and f(x) are the corresponding speed values.
Here, h = 5, the values from the table are:
- f(0) = 0
- f(5) = 1.22
- f(10) = 2.28
- f(15) = 4.12
- f(20) = 4.79
- f(25) = 5.39
- f(30) = 6.11
Applying the trapezium rule: $s \approx \frac{5}{2} \left( 0 + 2 \times 1.22 + 2 \times 2.28 + 2 \times 4.12 + 2 \times 4.79 + 6.11 \right)$ $= \frac{5}{2} \left( 0 + 2.44 + 4.56 + 8.24 + 9.58 + 6.11 \right)$ $= \frac{5}{2} \left( 30.93 \right) \approx 77.325.$

Thus, we can estimate that the train travels approximately 154.075 meters.

The speed, v m s⁻¹, of a train at time t seconds is given by v = \\sqrt{(1.2t - 1)}, \\ 0 \leq t \leq 30 - Edexcel - A-Level Maths Pure - Question 8 - 2006 - Paper 2

Worked Solution & Example Answer:The speed, v m s⁻¹, of a train at time t seconds is given by v = \\sqrt{(1.2t - 1)}, \\ 0 \leq t \leq 30 - Edexcel - A-Level Maths Pure - Question 8 - 2006 - Paper 2

Complete the table, giving the values of v to 2 decimal places.

Use the trapezium rule, with all the values from your table, to estimate the value of s.

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