Derivatives - Rates of Change: Problem 6 (1 point) The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s ( t ) = to - 6t2 + 9t + 2, t20 (a) Find the velocity and acceleration functions. v(t) : a(t): (b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent co, and U for the union of sets. Interval: (c) Over what interval(s) is the particle moving in the negative direction? Use inf to represent co, and U for the union of sets. Interval: (d) Over what interval(s) does the particle have positive acceleration? Use inf to represent co, and U for the union of sets. Interval: (e) Over what interval(s) does the particle have negative acceleration? Use inf to represent co, and U for the union of sets. Interval: (f) Over what interval is the particle speeding up? Slowing down? Use inf to represent co, and U for the union of sets. Speeding up: Slowing down:Derivatives - Rates of Change: Problem 10 (1 point) At a time t seconds after it is thrown up in the air, a tomato is at a height (in meters) of f(t) = -4.9t2 + 45t + 4 m. A. What is the average velocity of the tomato during the first 3 seconds? (Include units.) 30.3m/s B. Find (exactly) the instantaneous velocity of the tomato at t = 3. (Include units.) -17.4m/s C. What is the acceleration at t = 3? (Include units.) -9.8m/s^2 D. How high does the tomato go? (Include units.) 107.316m E. How long is the tomato in the air? (Include units.) -9.183s Note: You can earn partial credit on this problem. Preview My Answers Submit Answers I this 9 times