An elastomer is a polymer that can stretch and contract. in a perfect elastomer the force opposing extension is proportional to the displacement x from the resting state of the elastomer, so |f|=k_f x, where k_f is a constant. but suppose the restoring force weakens as the elastomer is stretched, and k_(f(x))=a-bx^(1/2) . evaluate the work done on extending the polymer from x = 0 to the final displacement of x = 1.

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.