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So, I was just wondering if in an isolated environment where there is no external force acting on the body and the body (with any mass) is pushed with a force such that it has a constant acceleration, so that would mean that the body's velocity will gradually increase with time and would never decrease (since body in motion stays in motion until an external force acts on it).

So, wouldn't this mean eventually it will reach velocity as same as light and even more and thus violating various laws of physics? Because lets say somewhere very very far into the universe there us bound to be an relatively isolated area and if we perform such an experiment wouldn't that cause some violations?

bm27
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  • @JohnRennie i don't have much knowledge into the relativity side of the things but what I understood is that the velocity will gradually increase and it will eventually come very close to c but never will be equal to it, as time to reach such an velocity would be so great that eventually it will never will be able to reach c. Is this correct? – bm27 Feb 05 '23 at 08:18
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    Correct. For us watching the accelerating spaceship from Earth we'll see the rocket approaching the speed of light but never quite reaching it no matter how long we wait. – John Rennie Feb 05 '23 at 08:21
  • Great! But does this argument apply for as great the initial velocity or acceleration (obviously not when equal to c) is? – bm27 Feb 05 '23 at 08:25
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    It makes no difference what the initial velocity is or what the acceleration is. Even if the rocket starts from $0.999999c$ it will still never reach $c$. – John Rennie Feb 05 '23 at 08:26
  • OK got it, thanks :D – bm27 Feb 05 '23 at 08:29
  • "Hyperbolic" motion is the special relativistic analogue of the usual "uniform acceleration" motion: https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity), see also https://physics.stackexchange.com/q/75487/226902 – Quillo Feb 05 '23 at 08:54
  • I show the derivation of the constant acceleration equation at the end of this answer: https://physics.stackexchange.com/a/345492/123208 – PM 2Ring Feb 05 '23 at 09:22
  • I'm not familiar with the relativity side of things and complex equations involving hyperbolic functions etc, but I understood the explanation provided by John Rennie, I hope to learn these things in the coming few years as I'm currently just in 10th grade and know physics at a relatively low level. – bm27 Feb 05 '23 at 09:34
  • Ah, ok. I assumed you knew some calculus, since you mentioned integrals in another question. You kinda need calculus to handle accelerations. You'll get to hyperbolic functions after a year or two of calculus. The Lorentz transformation (and the relativistic velocity addition formula) "only" need Pythagoras' theorem and simultaneous equations, but it does get a bit messy for anything beyond simple straight-line motion, so for more complicated motions we generally use matrices to keep it organised. – PM 2Ring Feb 05 '23 at 11:42

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