Integrating Velocity: Questions on Displacement & Position

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    Integrating Velocity
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Discussion Overview

The discussion revolves around the integration of velocity in the context of physics, specifically addressing whether integrating velocity yields displacement or position. Participants explore the implications of integration in both one-dimensional and multi-dimensional motion, as well as the relationship between displacement and position over time.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether integrating velocity results in displacement or position, suggesting that it is displacement based on the definition of integration as accumulated area.
  • Another participant confirms that integrating velocity gives displacement, noting that in one-dimensional motion, it results in a simple positive or negative displacement, while in multi-dimensional cases, it results in a displacement vector.
  • A follow-up question is raised about finding the exact position from a velocity graph, to which a participant responds that knowing the starting position and the displacement allows for determining the current position.
  • Further clarification is provided that integration involves setting limits to find displacement over a specific time interval, and that to find the actual position, one must consider the initial time.

Areas of Agreement / Disagreement

Participants generally agree that integrating velocity yields displacement, but there is a nuanced discussion about how to derive position from displacement, indicating that the discussion remains somewhat unresolved regarding the exact relationship between these concepts.

Contextual Notes

Some participants mention the importance of initial conditions and time intervals in determining position from displacement, highlighting the dependence on specific definitions and assumptions in the discussion.

opus
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Please see the attached image which are of my notes. In integrating acceleration, I have no confusions. But I have a specific question about integrating velocity.

When we integrate velocity, do we get the displacement of ##x##, or do we get it's position at a certain time?
I want to say it's the displacement as it's directly in the definition in green and integration is basically accumulated area. But I want to be sure.
Thank you.
 

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Yes it's the displacement. If the velocity is a scalar (one-dimensional motion) it's a simple positive or negative displacement. If it's a 2D or 3D velocity vector, we integrate each coordinate separately and get an overall 3D displacement vector as the result. Adding the displacement vector to the starting point in an affine sense gives us the position at the end of the journey.
 
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Ok thank you, so then is it possible to find exactly the position of ##x## when we have the graph of velocity?
 
opus said:
Ok thank you, so then is it possible to find exactly the position of ##x## when we have the graph of velocity?

If you know the starting position and you know the displacement, then you know the current position.
 
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Understood! Thank you.
 
opus said:
Please see the attached image which are of my notes. In integrating acceleration, I have no confusions. But I have a specific question about integrating velocity.

When we integrate velocity, do we get the displacement of ##x##, or do we get it's position at a certain time?
I want to say it's the displacement as it's directly in the definition in green and integration is basically accumulated area. But I want to be sure.
Thank you.
Actually during integration we set two limits t1 and t2 so that we get the displacement between the 2 time interval. After integration we gets the equation of displacement(with respect to time) of a particle . And when we sets the limit we get the displacement during that particular time interval. To find the actual position from origin you have to put t1=0. So we get its position as well as displacement from the origin. Thank you
 
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Excellent thank you.
 

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