2. The position function of an object is given by s(t) = 2t³ - 3t² - 12t + 8 where t 20. a) Find the velocity and acceleration functions. b) Find the time interval in which the object is moving in the positive direction. Find the time interval in which the object is moving in the negative direction. c) Sketch the path of the particle along a coordinate axis. d) Find the displacement and the distance traveled from t = 1 to t = 3. (Remember that distance refers to the actual ground that an object has covered during its motion. Displacement describes the overall change in position, or how far away and in which direction an object is from its original location.)

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