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Average acceleration = inst accleration ? 
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#1
Sep1004, 09:22 AM

P: 188

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 


#2
Sep1004, 09:42 AM

P: 403

What is the meaning of ' average' ?



#3
Sep1004, 10:28 AM

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PF Gold
P: 4,137

Let v_{1}=At for a time t_{1}
then v_{2}=Bt+At_1 for an additional time t_{2}. Then a_{1}=A and a_{2}=B. However, the [timeweighted] average acceleration is a_{avg}= (a_{1}t_{1}+a_{2}t_{2})/(t_{1}+t_{2})=(At_{1}+Bt_{2})/(t_{1}+t_{2}). 


#4
Sep1004, 02:01 PM

P: 188

Average acceleration = inst accleration ?
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. 


#5
Sep1004, 02:38 PM

Sci Advisor
PF Gold
P: 2,226

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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