Is acceleration correlated with an instantaneous velocity?

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Discussion Overview

The discussion revolves around the relationship between acceleration and instantaneous velocity, exploring whether acceleration is correlated with instantaneous velocity and how these concepts are defined in relation to time. The scope includes conceptual clarifications and technical explanations regarding the definitions and calculations of instantaneous and average acceleration.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that acceleration is the rate of change of velocity with respect to time.
  • It is noted that instantaneous acceleration, defined as dv/dt, determines how instantaneous velocity changes over an infinitesimal time interval.
  • One participant distinguishes between instantaneous acceleration and average acceleration, stating that average acceleration correlates to two velocities over a time interval, while instantaneous acceleration requires knowledge of the velocity function v(t) at every point within that interval.
  • There is a question raised about whether instantaneous velocity can be defined at any instant or if it is inherently changing.
  • Another participant emphasizes that to determine instantaneous acceleration, one must know the instantaneous velocity for every point in time within a given interval.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of instantaneous and average acceleration, but there is ongoing debate regarding the implications of these definitions, particularly concerning the nature of instantaneous velocity and whether it can be considered constant at a given instant.

Contextual Notes

Some participants highlight the need for knowing the instantaneous location to determine velocity, suggesting that without this knowledge, the concept of instantaneous velocity may not hold. This introduces uncertainty regarding the definitions and measurements involved.

gomer36
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Is acceleration correlated with an instantaneous velocity? tia
 
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yes, acceleration is the rate of change of velocity respect to time.
 
gsal said:
yes, acceleration is the rate of change of velocity respect to time.

thank you
 
Yes, since instantaneous acceleration is dv/dt, so this instantaneous acceleration determines how instantaneous velocity changes in an infinitesmall amount of time. i.e. the instantaneous acceleration determines how the instantaneous velocity changes in the vicinity of that instance.
 
Only instantaneous acceleration relates to instantaneous velocity. An average acceleration correlates to the two velocities of a time interval. For example if we have the time interval from [tex]t_1[/tex] to [tex]t_2[/tex] then the average acceleration for this time interval is [tex]a_{avg}=\frac{v_2-v_1}{t_2-t_1}[/tex] where v2 and v1 the velocities at time t2 and t1.

But to find the instantaneous acceleration we need to know the instanteneous velocity v(t) for every t inside (t1,t2) and not just only the two velocities v2 and v1 at the edges of the time interval t2 and t1. If we know v(t) then the instantaneous acceleration is [tex]a(t)=\frac{dv(t)}{dt}[/tex].
 
ZealScience said:
instantaneous acceleration determines how instantaneous velocity changes in an infinitesmall amount of time.

So, at any instant, can the instantaneous velocity be defined, or is it changing? (:devil:)
 
Delta² said:
But to find the instantaneous acceleration we need to know the instanteneous velocity v(t) for every t inside (t1,t2) and not just only the two velocities v2 and v1 at the edges of the time interval t2 and t1. If we know v(t) then the instantaneous acceleration is [tex]\frac{dv(t)}{dt}[/tex].

Similarly for velocity, we need to know the instantaneous location for every t inside an interval. If you know a location without also knowing what its location is at +Δt and -Δt then you cannot determine its velocity, but if you require a small interval of time to work out how it is moving, then it is no longer 'instantaneous'?!
 
cmb said:
So, at any instant, can the instantaneous velocity be defined, or is it changing? (:devil:)

Can be defined and its value at any instant t is v(t)
 

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