A particle is moved from point X to point Y under a force field. The work done depends only on the initial and final speeds. Which one of the following is correct?

The work–energy theorem states that the net work done on a particle equals the change in its kinetic energy: W = ΔKE = (1/2)m(v_f² - v_i²). Since kinetic energy depends only on the speed (not on direction or position), if the work done depends only on the initial and final speeds, this is exactly the work–energy theorem at play. A conservative force has work depending on positions (not speeds), so (a) is wrong. The force need not be constant, and velocity need not always increase. The correct interpretation is the work–energy theorem.