Average acceleration = inst accleration ?

Omid

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

Rogerio

What is the meaning of ' average' ?

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
a_avg= (a₁t₁+a₂t₂)/(t₁+t₂)=(At₁+Bt₂)/(t₁+t₂).

Omid

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

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.