PRO 3 No calculator is allowed for the following problem. A particle travels along the horizontal axis such that its velocity, v(t), in meters per second, at time t is given by the function u{t) = i100 12 for 0 s r s 20. The position of the particle is given by x(r}, and x(0) = 5. a) Find 1:112). Explain what this value indicates In terms ofthe context. b) Estimate the velocity of the particle at t = 12.1 seconds using a linear approximation at t = 12. c} Find the time k for which the average acceleration of the particle over the interval k s t s 20 is 1 misz. Justify your answer. d) Write, but do not solve, an equation that gives the time n at which the particle will be at a position of 100 meters. FRQ 4 No calculator is allowed for the following problem. 2+ O 31 Graph of f The function fis defined on the closed interval [-2, 6]. The graph of f consists of two quarter-circles and three lines segments, as shown above. Let g be the function defined by g(x) = [2 f(t) dt. a) Determine all values of x, besides x = 2, on the interval -2 s x 6 for which g(x) = 0. Justify your answer. b) For each of g(3), g '(3) and g "(3), find the value or state for which it does not exist. c) On what open interval(s) contained in -2