Suppose that the position function of a particle moving on a coordinate line is given by s(t) = ³-2t² + 3t - 7 in meters, where t is in seconds. (a) Find the velocity and acceleration functions; (b) Analyze the direction of the motion that shows when the particle is stopped, when it is moving forward and/or backward; (c) Analyze the change of speed that shows when it is speeding up and/or slowing down; (d) Find the total distance traveled by the particle from time t = 0 to t = 6 seconds.

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