Acd case slides along a floor in the positive direction of an x axis while an applied force a acts on it. the force is directed along the x axis and has the x component fax = 12x - 3x2, with x in meters and fax in newtons. the case starts at rest at the position x = 0, and it moves until it is again at rest.
(a) plot the work done on the case by a versus position x. (do this on paper. your instructor may ask you to turn in this work.)
(b) at what position is the work maximum?
(c) what is the maximum value of the work?
(d) at what position has the work decreased to zero?
(e) at what position is the case again at rest?

Your answer should be b if I’m not mistaken

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.