Let's say we have an object. And we then say that E = (1/2)mv(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}.

so we solve for velocity and say that

v = (2E/m)^(1/2)

then integrate both sides with respect to time

∫(2E/m)^(1/2)dt= ∫v dt

so we then have

(2E/m)^(1/2)t = distance

so if time was infinitely large (long) could an object travel an infinite distance if it was given in infinitesimally small unit of energy?

as i typed this out i realized that without an acceleration in obviously could but in my head this math means it's accelarating infinitely slow.

Don't hate me if this is wrong. I've only taken Calc 1 and high school physics. and I also have trouble explaining my scientific thoughts to others haha oh well. Please be indepth when denying my math. I also did substite E for (1/2)mv^2 at

∫(2E/m)^(1/2)dt= ∫v dt

this part but i got d = d^(1/2) for an answer. Thanks!

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# Infinte distance with finite energy?

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