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Work is not done when you carry an object forward. You may have learnt that carrying an object and moving horizontally at a constant velocity has no work done. The truth is, there is a slight amount of work done due to overcoming air resistance in the horizontal direction.
"No" according to the work energy theorem about work is done when there is a change in final and initial velocity. But if I use Work = Force x displacement, even though the velocity is constant there is still some displacement done by the (constant) force acting on it.
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