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The extrapolation of this Phys.SE post.

It's obvious to me that velocity can't be discontinuous, as nothing can have infinite acceleration.

And it seems pretty likely that acceleration can't be discontinuous either - that jerk must also be finite. All 4 fundamental forces are functions of distance so as the thing exerting the force approaches, the acceleration must gradually increase (even if that approach/increase is at an atomic, or sub-atomic level) e.g. in a Newton's Cradle, the acceleration is still electro magnetic repulsion to it's a function of distance, so it's not changing instantaneously, however much we perceive the contact to be instantaneous. (Even if we ignored the non-rigidity of objects.)

Equally I suspect that a force can't truly "appear" at a fixed level. Suppose you switch on an electromagnet, if you take the scale down far enough, does the strength of the EM field "build up" from 0 to (not-0) continuously? or does it appear at the expected force?

Assuming I'm right, and acceleration is continuous, then jump straight to the infinite level of extrapolation ...

Is motion mathematically smooth?

Smooth: Smoothness: Being infinitely differentiable at all point.

Community
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Brondahl
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    Possible duplicates: http://physics.stackexchange.com/q/151399/2451, http://physics.stackexchange.com/q/1324/2451 and links therein. – Qmechanic Nov 11 '16 at 17:42

3 Answers3

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Not a physicist, but I think acceleration can be discontinuous. Consider a car travelling at constant velocity (acceleration = 0) that hits a wall. De-acceleration (negative acceleration) commences until the car comes to a complete stop. For all intents and purposes over time t acceleration starts at zero, decreases to a negative value (because de-acceleration), and then instantaneously jumps back to zero.

My 2 cents.

Adam Shinbrot
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  • Hi, welcome to StackExchange. It's great to see new faces here, but I'm afraid this answer is just completely wrong. A car colliding with a wall doesn't start decellerating instantaneously. Apart from anything else "a car" isn't a thing with a single velocity or acceleration! And see my original question for arguments about why even a body that does appear to be close to an inelastic collision still isn't truely experiencing discontinuous acceleration. – Brondahl May 20 '19 at 21:54
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With respect, I think you're splitting hairs.

Before the wall, the velocity is constant, and a = 0. After the wall, the velocity is constant at 0, and a = 0. In between velocity is decreasing to 0, acceleration is the derivative of the velocity as a function of time, at some non-constant value of un-changing sign (since it's either constantly decelerating, or accelerating), so how does it start at 0, end at 0, and have some value of unchanging sign in-between without being discontinuous?

Adam Shinbrot
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  • Please don't post two answers like this. Fix your previous answer & delete this one. Or vice versa. ;) – PM 2Ring May 21 '19 at 21:16
  • On what grounds are you asserting that it's constantly decelerating? – Brondahl May 22 '19 at 05:47
  • I get it, thanks. I was assuming the acceleration graph was directional, downward slope deceleration, upward slope acceleration. (I don't know why I was assuming that). No, it's just an initial large amount of deceleration, then deceleration of lesser magnitude returning to zero. Thanks. – Adam Shinbrot May 22 '19 at 14:01
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acceleration cannot be infinite. Things need a force to be able to accelerate an object. So to infinitely accelerate and object it needs a infinite force. Also try wording question better.

Riley W. McNamara Cook
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