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Can the kinetic energy of an object/system change if no work is done
to/by the object/system?
It sure can. Imagine standing still on a frictionless surface and then
pushing off a wall to get yourself moving. Since the points of
application of either the force on you or the force on the wall do not
move, no work is done either on or by you. However, you do gain kinetic
energy as you slide away from the wall.