Equations of Motion.The position of a particle between t = 0.00s and t = 2.00s is given by x(t) = At^3 + Bt^2 + Ct, where A = 3.00 m/s^3, B =-10.0 m/s^2, and C = 9.00 m/s. * Sketch the x-t, vx-t, and ax - t graphs over this time interval. (3) * At what time (s) is this particle at rest in this time interval? (2) * At each of the times found in b), is the acceleration of the particle positive or negative? Show that in each case the answer is the same whether deduced from vx-t graph or the function for ax(t). (2) * What is the particle's greatest displacement from the origin during this time interval? (1) * At what time in this interval is the particle speeding up at its greatest rate? At what time in this interval is the particle slowing down at its greatest rate? (2)