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The speed, v m s^-1, of a train at time t seconds is given by v = √(1.2t - 1), 0 ≤ t ≤ 30 - Edexcel - A-Level Maths Pure - Question 7 - 2006 - Paper 2
Question 7
The speed, v m s^-1, of a train at time t seconds is given by v = √(1.2t - 1), 0 ≤ t ≤ 30. The following table shows the speed of the train at 5 second intervals. ... show full transcript
Worked Solution & Example Answer:The speed, v m s^-1, of a train at time t seconds is given by v = √(1.2t - 1), 0 ≤ t ≤ 30 - Edexcel - A-Level Maths Pure - Question 7 - 2006 - Paper 2
Step 1
Complete the table, giving the values of v to 2 decimal places.
Answer
To complete the table, we use the formula v = √(1.2t - 1) to calculate the missing values at t = 15, 20, and 30 seconds:
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For t = 15:
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For t = 20:
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For t = 25:
Thus, the completed table is:
t 0 5 10 15 20 25 30 v 0 1.22 2.28 4.24 4.79 5.38
Step 2
Use the trapezium rule, with all the values from your table, to estimate the value of s.
Answer
We apply the trapezium rule to estimate s:
Using the values from the table: 0, 1.22, 2.28, 4.24, 4.79, 5.38, 6.11.
The formula for the trapezium rule is:
S = rac{h}{2} (y_0 + 2y_1 + 2y_2 + 2y_3 + 2y_4 + 2y_5 + y_6) where h = 5 (the interval) and the y-values are those calculated earlier.
Calculating each step:
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S = rac{5}{2} [0 + 2(1.22) + 2(2.28) + 2(4.24) + 2(4.79) + 2(5.38) + 6.11]
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Substituting: = rac{5}{2} [0 + 2.44 + 4.56 + 8.48 + 9.58 + 10.76 + 6.11]
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Summing: = rac{5}{2} [42.93] = 107.325
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Therefore, the estimated distance s is approximately 154.075, rounding gives: