Average acceleration = inst accleration ?


by Omid
Tags: acceleration, accleration, average, inst
Omid
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#1
Sep10-04, 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
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Rogerio
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#2
Sep10-04, 09:42 AM
P: 403
What is the meaning of ' average' ?
robphy
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#3
Sep10-04, 10:28 AM
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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).

Omid
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#4
Sep10-04, 02:01 PM
P: 188

Average acceleration = inst accleration ?


Quote Quote by robphy
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.
jcsd
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#5
Sep10-04, 02:38 PM
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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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