show all work and use number lines and diagrams if needed

Given the position function s(t) = -(2x - 5)(x - 1)(x - 6) represent the position, in metres, of an object as it travels in a straight line with respect to time, in seconds. Determine the following for 0 S t - 7: a. Find the object's velocity, v(t), and acceleration, a(t), at time, t. [3] b. What is the position of the object at the halfway through the interval? [2] c. Determine the time(s) when the object changes direction. [3] d. Determine the intervals when the object is speeding up. [4] e. What it the total distance travelled over the interval? [4]