Average acceleration = inst accleration ?

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Homework Help Overview

The discussion revolves around the relationship between average acceleration and instantaneous acceleration, exploring whether they can differ at any point in time. The subject area includes concepts from both physics and calculus.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definitions of average and instantaneous acceleration, with some referencing the Mean Value Theorem. Questions arise regarding the conditions under which average acceleration can differ from instantaneous acceleration.

Discussion Status

The discussion is ongoing, with participants expressing differing views on the relationship between average and instantaneous acceleration. Some guidance has been offered regarding the conditions under which these accelerations may be equal, particularly in the absence of discontinuities.

Contextual Notes

There is a mention of the Mean Value Theorem and its implications for the problem, as well as a focus on the definitions and interpretations of average acceleration in the context of time intervals.

Omid
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Can the average acceleration of a body be not equal to the instantaneous acceleration for at least an instant?


I know the answer to the question above is NO. But I find the answer; using Mean value theorem in calculus.
Let me know if there is any answer based on physics.
Thanks
 
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What is the meaning of ' average' ?
 
Let v1=At for a time t1
then v2=Bt+At_1 for an additional time t2.
Then a1=A and a2=B.
However, the [time-weighted] average acceleration is
aavg= (a1t1+a2t2)/(t1+t2)=(At1+Bt2)/(t1+t2).
 
Last edited:
robphy said:
Let v1=At for a time t1
then v2=Bt+At_1 for an additional time t2.
Then a1=A and a2=B.
However, the [time-weighted] average acceleration is
aavg= (a1t1+a2t2)/(t1+t2)=(At1+Bt2)/(t1+t2).


Sorry, I don't see any relation between your answer and my question.
I meant in a given time interval is it possible for a body to has average acceleration 'a' but never reach it as instantaneous acceleration.
 
II'm not sure what question your asking, but within in a given inertval there will always be an instant when the acceleration is equal to the avergae accelartion within that inertval as long as there are no discontinuities in the accelartion as a function of time within that interval.
 

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