6   2. A particle P is moving along the x-axis. At time t seconds, t  0, P has acceleration a m s–2 and velocity v m s–1 in the direction of x increasing, where v = e2t + 6et – kt and k is a positive constant. When t = ln 2, a = 0 (a) Find the value of k. (4) When t = 0, the particle passes through the fixed point A. When t = ln 2, the particle is d metres from A. (b) Showing all stages of your working, find the value of d correct to 2 significant figures. [Solutions relying entirely on calculator technology are not acceptable.] (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 7   Question 2 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 2 is 8 marks)