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 correct answer is B, the net work equals the change in kinetic energy. A work done that is fixed by the starting and ending speeds alone is exactly what the work-energy theorem states: W(net) = ½mv² − ½mu².

The work-energy theorem follows from Newton's second law and holds for every kind of force, constant or varying, conservative or not. Whatever path the particle takes from X to Y, the total work done on it by all forces equals its gain in kinetic energy, so only its initial speed u and final speed v matter. If the particle slows down, the net work is simply negative.

A is wrong because a conservative force is one whose work depends only on the start and end positions, through potential energy; nothing here says that, and the theorem holds for non-conservative forces too.

C is wrong because the theorem needs no constant force; it holds for any force.

D is wrong because the speed can fall as well as rise; then the work done is negative.

Exam tip: net work = change in kinetic energy (speeds); conservative force work = minus change in potential energy (positions).