Let's say we have an object. And we then say that E = (1/2)mv2. 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!