Condition for Instantaneous Acceleration = Average Acceleration

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Homework Help Overview

The discussion revolves around the conditions under which instantaneous acceleration equals average acceleration, as illustrated by a graph. Participants are exploring the relationship between these two concepts in the context of motion and acceleration.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster seeks clarification on how to determine if instantaneous acceleration equals average acceleration, referencing a specific graph. Some participants discuss the conditions under which average and instantaneous values may coincide, particularly in relation to the continuity and monotonicity of the changing quantity.

Discussion Status

Participants are actively engaging with the concepts, with some providing insights into the conditions for equality between average and instantaneous acceleration. There is an exploration of different interpretations regarding when these values may be equal, but no consensus has been reached.

Contextual Notes

There is an emphasis on understanding the behavior of quantities over time intervals, and the discussion includes considerations of how these quantities change, particularly in relation to the graph referenced by the original poster.

navneet9431
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Homework Statement



IMG_20180701_220442.jpg
[/B]
Look at this graph.Is Instantaneous Acceleration=Average Acceleration here?
Please explain your solution.
What should be done to check whether Average Acceleration=Instantaneous Acceleration?

Homework Equations


Average Acceleration motion equations

The Attempt at a Solution


I know that Average Acceleration = (Final Velocity-Initial Velocity)/Time Interval
I can't proceed further.
I will be thankful for any help!

 

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When a quantity is changing continuously within a time interval its average value is equal to its instantaneous value only once. When a quantity is constant over a time interval, its average value is always equal to its instantaneous value. Does that help? Read the graph.

On edit: Also see correction below.
 
Last edited:
kuruman said:
When a quantity is changing continuously within a time interval its average value is equal to its instantaneous value only once.
... if it is changing monotonically, that is.
 
haruspex said:
... if it is changing monotonically, that is.
Yes, thanks. Instead of "always", I should have said "only at certain times".
 

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