Consider a hypothetical empty universe containing a single object. Given an initial push, will the work done by the forever moving object be infinite?
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$\begingroup$ If the Universe contains only a single object, then there is nothing to push against and no way of detecting motion. This is related to something called Mach's principle ... "If all motion is relative, how can we measure the inertia of a body? We must measure the inertia with respect to something else. But what if we imagine a particle completely on its own in the universe? ... Mach's principle is sometimes interpreted as the statement that such a particle's state of motion has no meaning in that case." en.wikipedia.org/wiki/Mach's_principle $\endgroup$– Peter WebbCommented Mar 2, 2015 at 17:26
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Work is done as long as the force is applied on the body, so in this case, the total work done would be the product of Force applied and the Displacement during the initial push only. If the object moves forever, it would do so with a constant velocity in this scenario, and consequentially its Kinetic Energy would be constant, implying that the work done after the initial push is zero. (Since $W=\Delta K.E$)
answered Mar 2, 2015 at 17:17