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Is it theoretically possible for an object or particle to change to the opposite direction without making a complete stop first?

Lets say I have a fictional hammer swing setup like this:

Hammer swing setup

I fire an electron to the hammer and the hammer smashes it back, is it possible for the electron (or any other particle or body) to change direction without slowing down and making a complete stop? If not, which law defines that?

Note: the question isn't about the hammer part but that was just the first thing that came up in my mind.

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  • $\begingroup$ Does the bug stop, even for a millisecond, when it hits your windshield? It's an old question but the same idea, I think. $\endgroup$
    – user108787
    Sep 6, 2016 at 19:24
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    $\begingroup$ Ever made a rolling u-turn in a car? Did you end up going the opposite direction? Did you stop? $\endgroup$ Sep 6, 2016 at 19:36
  • $\begingroup$ Because of link rot, avoid linking to images. Instead directly upload them. $\endgroup$
    – Gert
    Sep 6, 2016 at 21:56
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    $\begingroup$ @Gert, I just learned a new term: "link rot". That's a "good one". Regarding the OP's question, if you fire a projectile into a U shaped tube, you can get an object to reverse direction without first coming to a stop. $\endgroup$ Sep 7, 2016 at 1:27

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No, it's not possible. An instantaneous velocity change implies an infinite acceleration. An infinite acceleration would require an infinite force.

(Some of the comments point out that you can do a U-turn, in which case the velocity is reversed without ever being zero, but I think you are asking about straight line motion.)

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    $\begingroup$ I'm not convinced by this, because the question is asking whether velocity has to be a continuous function of time (or at least satisfies the Intermediate Value Theorem), and your answer starts off by assuming that velocity is a differentiable function of time (so that we can talk meaningfully about acceleration). If the OP is unwilling to assume continuity, why should he be willing to assume differentiability? $\endgroup$
    – WillO
    Mar 28, 2017 at 3:55
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You have to consider that velocity is a vector - magnitude and direction. If the particle has a specific velocity and you want it to change to the negative (same magnitude, exact opposite direction) then it has to stop completely in the original direction of motion. It can follow a curved path and never stop moving, but the velocity in the original direction of motion will have to come to zero before it starts moving back in the opposite direction.

If it is moving in the X direction originally with velocity Vx, then it can curve through the Y (or Z) direction with velocity Vy or Vz, and never stop, but at the instant when it is traveling at right angles to the original X direction, then Vx is zero. It's stopped in that direction.

As for the bug on the windshield, all parts of the bug have to come to a stop before reversing direction. They just don't all stop at the same time - which is why windshields are bad for bugs.

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Consider a theoretical crankshaft, con rod and piston: the crank rotates continuously and transfers rotational motion into linear motion via the con rod to the piston. Given that the crank is in continual motion how can the piston be motionless at the top and bottom of the 'stroke'? Another means of imagining the concept of a reversal of direction without stopping is to visualise a point of light revolving around a circle as viewed from above. Now visualise that circle from the side: the point of light will be seen to travel from left to right and back again. Does it stop at each extremity?

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I think I understand your question, where the particle is in linear motion and whether or not it can instantaneously change direction without deceleration/acceleration? I don't know the proper answer myself and can only assume that the material would have to have absolutely zero elasticity or give in the material.

The only other option I can think of is a wormhole in the path of the particle where the other end is in the same position of the $x-$axis but directs the particle to come out at the same speed but in the opposite direction. This would give a perfectly vertical line from positive velocity the same negative velocity on a velocity vs time graph.

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Yes an object must stop in order to change direction 180 degrees. This means that the object it “hits” must also stop. So when an object (small steel ball) strikes another object (the windshield of a moving car) both objects stop. This causes vibration in the form of sound waves and heat and in some conditions the object(s) to break-up.

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Yes, it is possible to pass through zero velocity without stopping. The electron in your example can't stop because, at the point of reversing direction, it would be in contact with the far heavier hammer. Obviously, the hammer doesn't stop its rotation therefore the electron must reverse direction instantaneously. In other words, how can the mass of an electron affect the mass of a hammer in motion?

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  • $\begingroup$ Instantaneous zero velocity = instantaneous rest is still instantaneous stopping. That is simply the definition of those English terms. $\endgroup$ Apr 23, 2023 at 4:34
  • $\begingroup$ Not really. The definition of stopping is; a cessation of movement or operation. I'm asserting that the electron does not stop even though it passes through zero velocity, it is in constant motion. $\endgroup$ Apr 24, 2023 at 2:27
  • $\begingroup$ Cambridge: to pause for a short time while travelling or during an activity. Oxford: to end an activity for a short time in order to do something. MW: a halt in a journey. $\endgroup$ Apr 24, 2023 at 3:02
  • $\begingroup$ And it is also necessary to physics. When one throws an object directly upwards and it is accelerated downwards by gravity, the object comes to a momentary stop at the top of its motion. We need to have some way to talk about that. Typically students would object to it having that momentary stop, but it is easy to point out that the velocity time graph shows a straight line that passes through zero, and thus by continuity it must have a point that is exactly zero. That is the momentary stop. $\endgroup$ Apr 24, 2023 at 3:19
  • $\begingroup$ But, in reality, that zero velocity instant also has zero time, therefore it doesn’t stop. $\endgroup$ Apr 24, 2023 at 10:39

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