Average Velocity and Constant Acceleration

AI Thread Summary
The formula Vav=(Vi+Vf)/2 is not exclusively valid for constant acceleration, as it can also apply to variable acceleration under certain conditions. A graph of velocity versus time illustrates that the area under the curve represents distance traveled, which can be the same for different velocity functions. If the area under the curve from initial to final velocity remains constant, the average velocity will also remain the same. Thus, the average velocity can be derived from various shapes of velocity-time graphs, not just those representing constant acceleration. This demonstrates that the average velocity formula is more versatile than initially suggested.
Ali Asadullah
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Can some one please prove that Vav=(Vi+Vf)/2 is valid only for constant acceleration?
 
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Ali Asadullah said:
Can some one please prove that Vav=(Vi+Vf)/2 is valid only for constant acceleration?
No, because it isn't valid only for constant acceleration. There are other velocity functions that also yield this average velocity.
 
Ali Asadullah said:
Can some one please prove that Vav=(Vi+Vf)/2 is valid only for constant acceleration?
It's posible for Vav=(Vi+Vf)/2 to be true for variable acceleration as well. Start off with a graph of velocity (y axis) versus time (x axis). Then the area below the horizontal line that goes from {t0, Vav} to {t1, Vav} = Vav x (t1 - t0) = the distance traveled. Then note that any line of any shape with the same amount of area under the line from {t0, Vi} to {t1, Vf} would also have the same average velocity as constant acceleration.
 

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