Is it possible to have zero velocity and zero acceleration?

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Discussion Overview

The discussion revolves around the question of whether it is possible for an object to have both zero velocity and zero acceleration while still being considered a moving object. Participants explore various definitions of "moving," the implications of instantaneous states of motion, and the mathematical interpretations of velocity and acceleration.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that an object can have zero velocity and zero acceleration at a specific moment, such as at t=2 for the trajectory x=(t-2)^3.
  • Others challenge the definition of "moving," suggesting that it implies a continuous change in position, and thus having zero velocity means the object is not moving at that instant.
  • A participant argues that an object can be considered moving if it has a trajectory that includes periods of zero velocity, such as stopping momentarily before continuing its motion.
  • Some participants emphasize the mathematical definitions of velocity and acceleration, noting that acceleration is the derivative of velocity and questioning how these concepts apply at specific points in time.
  • There is a discussion about frames of reference, with some suggesting that an object can be considered moving in one frame while being stationary in another.
  • Participants express differing views on whether it is contradictory to say an object can be stationary in a frame while also moving in another frame.
  • One participant presents a formal definition of "moving" based on the continuity of position over time, suggesting that an object can be moving over an interval while having zero velocity and acceleration at a specific point within that interval.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions of "moving" and the implications of having zero velocity and acceleration. Multiple competing views remain, with some arguing for a strict interpretation of motion and others allowing for exceptions based on mathematical definitions.

Contextual Notes

There are unresolved assumptions regarding the definitions of motion, velocity, and acceleration, as well as the implications of instantaneous states of motion. The discussion reflects a range of interpretations and mathematical reasoning that may not align.

  • #31
persia77 said:
does it have instantaneous zero velocity and instantaneous zero acceleration simultaneously?

Yes, I stipulated that:
jbriggs444 said:
Exactly as the puck achieves zero velocity, the electric field reaches zero and begins increasing in the northward direction.
 
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  • #32
A.T. said:
If your definition of "moving" doesn't even require a direction, what physical relevance does your definition of "moving" have, and why should we even care about that type of "moving"?
direction is zero at instantaneous zero velocity :)
 
  • #33
persia77 said:
direction is zero at instantaneous zero velocity :)

The normal definition of the "direction" of a vector quantity would involve the vector being divided by its magnitude. The result has a magnitude of 1 and may be referred to as a "unit vector" or "direction vector". In the case of a zero vector, this involves division by zero. The direction of the zero vector is not defined.
 
  • #34
persia77 said:
direction is zero
Sounds like your definition of "direction" is just as useful as your definition of "moving".
 
  • #35
A.T. said:
Sounds like your definition of "direction" is just as useful as your definition of "moving".
useful for u
 
  • #36
I don't think more posts would add any value to this thread. It depends on the definition of "moving", so there is no general answer, and all the different cases have been discussed. Closed.
 

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