Proving Constant Acceleration's Impact on Average Velocity

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Homework Help Overview

The discussion revolves around proving the relationship between constant acceleration and average velocity, specifically the formula average velocity = (vf + vi) / 2. The subject area is kinematics within physics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to validate the formula by drawing a diagram and calculating average velocity. Some participants question whether this approach is sufficient or if alternative methods exist. Others suggest using calculus or graphical interpretations to support the claim.

Discussion Status

The discussion is active, with participants exploring different methods to prove the relationship. There is an exchange of ideas regarding the use of calculus and graphical representations, but no consensus has been reached on a definitive approach.

Contextual Notes

Participants are considering the implications of constant acceleration and the assumptions that come with it, such as the linearity of the velocity-time graph.

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Homework Statement



Prove that if the acceleration is constant, the average velocity=vf+vi/2

Homework Equations


average velocity=xf-xi/change in t
xf=xi+vit+1/2at^2
vf^2=vi^2+2a(xf-xi)



The Attempt at a Solution



I started out by drawing a diagram:

_ _ _ _ _ _ _ _ _
Vi v vf
20km/h 20km/h

20+20/2=20

Do you think this proves it or is there another way of doing it?

Thank you in advance
 
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Could someone please help me on this?

Thank you very much
 
Can you use calculus or not?
 
vf = vi + at
Now if a=constant, the graph of velocity plotted against time is a straight line, yes? (From the equation above)
Now it is obvious that the average velocity between vf and vi must be (vf + vi)/2 from the graph.
Otherwise you can use calculus to find the time average of the velocity function.
 
Thank you very much

Regards
 

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