I know we only go close to zero, not equal zero, but if that somehow happens, will it be zero as it is at rest or 35mps as when you resume the time, the speed is 35mps?
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2$\begingroup$ "If that somehow happens," then our current understanding of physics does not apply, so there's no way to answer your question. $\endgroup$– J. MurrayCommented Jul 7, 2023 at 15:07
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2$\begingroup$ Are you asking how instantaneous velocity is defined? $\endgroup$– John RennieCommented Jul 7, 2023 at 15:11
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$\begingroup$ I'm not quite sure what you're asking, but I suspect that it's similar to this question: physics.stackexchange.com/q/475703/123208 $\endgroup$– PM 2RingCommented Jul 7, 2023 at 16:03
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3$\begingroup$ I believe you have rediscovered Zenos arrow paradox. Se for example here: plato.stanford.edu/entries/paradox-zeno/#Arr $\endgroup$– user330563Commented Jul 8, 2023 at 8:50
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1$\begingroup$ Ok. We have some old questions on the theme of "is there anything that velocity does to an object that's detectable in an instantaneous snapshot?" Eg, physics.stackexchange.com/q/609198/123208 & physics.stackexchange.com/q/508066/123208 $\endgroup$– PM 2RingCommented Jul 10, 2023 at 6:10
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2 Answers
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The closest thing I can think of to what you're asking would be to ask, in physics language, "does the state of an object at a given time involve just its position, or both its position and its velocity?"
In other words, imagine writing a computer program that will do a physics simulation, using the laws of physics to figure out what should happen in a given scenario. The question is equivalent to "In addition to the laws of physics, do we need to tell the computer only where all the objects are to start, or where they are, plus how they are moving to start?"
The answer is that you need to tell the computer both where objects are and how they are moving in order for the simulation to make accurate predictions. In classical physics, we model the state of an object using both its position and its velocity (or sometimes using both its position and its momentum, but this is essentially the same thing).
In this sense, if you could "freeze time", objects would still have a velocity. At least, if we took the way that the computer represented objects at any time, it would have to record both the position and the velocity of every object. Alternatively, if we had a pencil-and-paper model of the motion, then we wrote down a complete summary of the system at some particular time $t,$ we would write down both the positions and the velocities.
This is a consequence of the specific laws of classical physics. We use Newton's laws to calculate the acceleration of each object in a system as a function of the state of the system. The acceleration is how fast the velocity is changing, not the velocity itself. This means the physical laws do not directly tell us the velocity at a given time in terms of positions alone. We must add the velocities in as additional information with the positions before we can use the laws of physics to find what will happen next.
This is the closest analogy I can think of in physics to the question of what properties an object has with time frozen.
This answer only describes classical physics. In quantum mechanics, the situation is more complicated. The state of the system is neither a position nor a velocity, but a different thing altogether. It is different enough that I can't think of any acceptable analogy to your question in quantum physics, except to say that the state of a system in quantum mechanics gives information about velocity just as well as it does about position, so that, as a loose analogy, you could say that in quantum mechanics things have a velocity when time is frozen just as much as they have a position when time is frozen. But again, this is a rather loose analogy, people might argue with it on technical grounds, and it is just the best I can do right now in making a loose analogy.
answered Jul 7, 2023 at 15:26
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If an object is travelling at say 35 mph, if I somehow stop the time, is the speed zero or 35 mps?
Given this then what is the speed at t=0? It is 35 mph. The speed is an unchanging constant.
