Condition for Instantaneous Acceleration = Average Acceleration

In summary, the conversation is about determining whether instantaneous acceleration is equal to average acceleration. The speaker explains that when a quantity is changing continuously within a time interval, its average value is equal to its instantaneous value only once. They also clarify that this is only true if the quantity is changing monotonically. The speaker adds that they are unable to proceed further and ask for help.
  • #1
navneet9431
Gold Member
107
9

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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  • #2
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:
  • #3
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.
 
  • #4
haruspex said:
... if it is changing monotonically, that is.
Yes, thanks. Instead of "always", I should have said "only at certain times".
 

Related to Condition for Instantaneous Acceleration = Average Acceleration

1. What is the condition for instantaneous acceleration to equal average acceleration?

The condition for instantaneous acceleration to equal average acceleration is when an object undergoes uniform acceleration, meaning that its velocity changes by the same amount in each unit of time.

2. Why is it important for instantaneous acceleration to equal average acceleration?

This condition is important because it allows us to simplify the calculation of acceleration by using the average velocity over a given period of time instead of having to measure the exact velocity at a specific moment in time.

3. How can this condition be applied in real-world situations?

This condition can be applied in various real-world situations, such as calculating the acceleration of a car during a race or the acceleration of a falling object due to gravity. It allows us to analyze and understand the motion of objects in a more efficient manner.

4. Can instantaneous acceleration ever be greater than average acceleration?

Yes, instantaneous acceleration can be greater than average acceleration when an object undergoes non-uniform acceleration, meaning that its velocity changes by different amounts in each unit of time.

5. Is this condition always true for all types of motion?

No, this condition is not always true for all types of motion. It only applies to objects undergoing uniform acceleration. For objects with non-uniform acceleration, the condition does not hold and the instantaneous acceleration will not equal the average acceleration.

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