Suppose that the position function of a particle moving on a coordinate line is given by s(t) =t3-9t2+24t 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.