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What speed is something moving at right before it stops?

  1. Dec 18, 2008 #1
    I am totally new to physics and do not study it what so ever. I do however find it extremely interesting and one question that has always puzzled me is -

    If some thing is moving and it comes to a complete stop, at what speed was it travelling at right before it stops?

    what ever speed you come up with surely you can half that speed again and again.

    The only conclussion i can come up with is that it never actually stops or it's never moving to begin with.

    Someone please help me with this. Share your thoughts with me. If you think I am talking rubbish please tell me with an explanation as to why.


  2. jcsd
  3. Dec 18, 2008 #2


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    The problem is, what do you mean by "right before"? Whatever amount of time you pick before the time it stops, you can half that time again and again too. For example, if it was decelerating at 1 meter/second^2, then 1 second before it stopped it was moving at 1 meter/second, 0.5 seconds before it stopped it was moving at 0.5 m/s, 0.25 seconds before it stopped it was moving at 0.25 m/s, etc.
  4. Dec 18, 2008 #3
    exactly right! this is just another part of the question with the same meaning. i have tried to understand this one too. it all makes my head hurt lol

    so my question still stands......does it actually ever stop?
  5. Dec 18, 2008 #4


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    If both time and speed are infinitely divisible, what's the problem? At every precise time you can identify a precise speed, and there is a precise time when the speed is 0 m/s. The fact that there is no "last time it's still moving" is just a consequence of this infinite divisibility, it's like asking "what's the largest real number less than 2"? 1.99 is a real number less than 2, 1.9999 is a larger real number less than 2, 1.999999999 is an even larger real number less than 2, etc. In real analysis the set of all real numbers less than 2 is what's called an open set, basically meaning that the "edge" of the set (in this case 2) is not itself a member of the set, and likewise the set of times before a moving object stops would be an open set.
  6. Dec 18, 2008 #5
    Your question sounds a lot like Zeno's paradox. Here are some solutions.
  7. Dec 18, 2008 #6
    With some certainty it would be equal or less than the speed of light.
  8. Dec 18, 2008 #7


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    Hi Dave, Welcome to PF.

    The correct term for the velocity right before it stops is "infinitesimal". I don't know if you have taken any calculus yet, but once you learn about limits, infinite, and infinitesimal then Zeno's paradoxes are resolved clearly.
  9. Dec 19, 2008 #8


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  10. Dec 19, 2008 #9


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    No, that wasn't your question before. In your first post you stated that the object stopped and asked what was it speed "just before it stopped". The answer, and what JesseM said, is that that question is too vague to be answered. You would have to tell us what you mean by "just before".

    And calculus, as it is normally taught to undergraduates, uses limits, NOT "infinitesmals". You can use infinitesmals in "non-standard analysis" but that requires deep results from symbolic logic.
    Last edited: Dec 19, 2008
  11. Dec 19, 2008 #10
    i think what you are really asking is

    " at what point in time does one event stop and another start" interesting question?

    i would say in your case " it stops when you cannot measure any more motion"
  12. Dec 19, 2008 #11


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    So then how big is "dx" in an integral as normally taught to undergraduates? I learned about the concept of infinitesimal in high-school level calculus.
  13. Dec 19, 2008 #12
    Thanks guys for all your comments. This has opened up a particular vague question on my part to a whole new way of thinking.

    My facination on this subject grows stronger!
  14. Dec 19, 2008 #13
    If you ask me, not only is everything always moving, but it is always moving with non-constant velocity, non-constant acceleration, etc. Things are in a perpetual state of change... so if x(t), x'(t), x''(t), ..., nth derivative of x(t), ... are all non-constant OR after some nth derivative they are all always constant.

    So I agree with you. I posted a related question in the general math section... called "I could use some help with a proof" or something... posted on Dec. 19.
  15. Dec 19, 2008 #14


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    While the philosophy of this question is all good fun, I will revert back to physics and suggest to you an actual, nonzero, concrete (albeit "blurry") speed: greater than or equal to 1 fm/s. Then, since I suspect that you don't believe me, I turn the question back around to you and ask, in the spirit of science, "what experiment do you propose to disprove this?" I.e., what experiment do you propose to prove that an object can achieve a speed less than 1 fm/s before coming to a complete stop? While I may not be entirely devoted to this claim, I hope that you use this as an oportunity to appreciate the distinction and cooperation between philosophy and science.
  16. Dec 19, 2008 #15


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    Now to me, this does sound like a different perspective on the same question. The speed of an object at any given time depends on the "given time." Asking what the speed is "just before" its stops is very similar to asking what the time is "just before" it stops. Whether there is such a thing as a "lowest speed" before stopping is sort-of the same question as whether there is a "last momemt" before stopping.

    This is one of the ways in which quantum mechanics seeks to solve some of the oldest problems of science and philosophy. If time is quantized, and space is quantized, then velocity and acceleration can be, too. If that is true, then there can be such a thing as a "last moment" and a "slowest speed."
  17. Dec 20, 2008 #16
    In my opinion: things never completely stop. matters have heat and heat is an energy related to motion, and as I know: harmonic ( sinusodial ) motion ( vibration ) so all derivatives of this motion related to heat are also sinusodials.

    when the object is moving with high speed, a big component of its motion is directed and lets say 20m/s south and ~5 micrometer/s sinusodial ( heat, magnitute totally made-up... have no idea ).

    but when it is close to stopping, big component of its motion will be the sinusodial heat related motion and magnitute of directed motion will not matter much.

    so the object will never reach to a state where all its kinetic energy is gone.
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