Edexcel Mathematics June 2022 · Paper 1 · Question 8 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

June 2022 · Paper 1 · Question 8 · 8 marks

8. v t T O Figure 2 Acarstopsattwosets of traffic lights. Figure 2 shows a graph of the speed of the car, v m s−1, as it travels between the two sets of traffic lights. The car takes T seconds to travel between the two sets of traffic lights. The speed of the car is modelled by the equation v = (10 − 0.4 t) ln (t + 1) 0  t  T where t seconds is the time after the car leaves the first set of traffic lights. According to the model, (a) find the value of T (1) (b) show that the maximum speed of the car occurs when t = 26 11++ln()t − 1 (4) Using the iteration formula tn +1 = 26 11++ln()tn − 1 with t1 = 7 (c) (i) find the value of t3 to 3 decimal places, (ii) find, by repeated iteration, the time taken for the car to reach maximum speed. (3) 17 18 19

Lesson: Laws of Indices