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$\begingroup$ Do you mean applying a force for a limited finite duration or applying a force forever? $\endgroup$– Vincent ThackerCommented May 2 at 16:38
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$\begingroup$ In this post I was talking about applying force for a limited finite duration. But I don't think there's a difference between the two; since our object is on a frictionless surface the object should approach infinity regardless of how much force is applied to it over what period of time based on Newton's First Law of Motion. $\endgroup$– ryangoslingCommented May 2 at 16:41
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2$\begingroup$ 1. There is no speed greater than c. 2. There is no "any amount of force". How do you imagine it? $\endgroup$– trulaCommented May 2 at 16:48
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1$\begingroup$ Does this answer your question? Can infinite work be done? $\endgroup$– DaleCommented May 2 at 16:58
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$\begingroup$ Every object now and then has limited amount of total energy which is bounded by condition : $$\sqrt{\frac {E_{tot} } {\gamma m} } \leq c$$. Your problem is that you include not that distance in work calculation - it must be distance over which force is applied, not total covered distance by body. $\endgroup$– Agnius VasiliauskasCommented May 2 at 17:03
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