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Can an object accelerate to infinite speed in a finite time-interval (Newtonian)in non-relativistic Newtonian mechanics?

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Can an object accelerate to infinite speed in FINITEa finite time-interval (Newtonian)?

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Can an object accelerate to infinite speed in FINITE time (Newtonian)?

Obviously this is impossible in relativity; however, if we ignore relativity and use only Newtonian mechanics, is this possible? How (or why not)?