A particle is moving along the x-axis with an acceleration function a(t) = 2t - 5, where a is in meters, and t is in seconds. If you know that the initial velocity is 6 m/sec and initial displacement is 1 meter, determine the following. a. Determine when the distance from the origin goes from increasing to decreasing on the interval from t = 0 tot = 12 seconds. b. Find the displacement of the particle on the time interval from t = 0 to t = 12 seconds. c. Find the total distance travelled by the particle on the time interval from t = 0 to t = 12 seconds. d. Find the position of the point at time t. (ie. find s(t) the position function)