Average Velocity and Constant Acceleration

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SUMMARY

The formula Vav = (Vi + Vf) / 2 is not exclusively valid for constant acceleration; it can also apply to variable acceleration scenarios. The discussion highlights that the average velocity can be derived from the area under the velocity-time graph, indicating that any velocity function with the same area will yield the same average velocity. This conclusion emphasizes the broader applicability of the average velocity formula beyond constant acceleration cases.

PREREQUISITES
  • Understanding of basic kinematics concepts
  • Familiarity with velocity-time graphs
  • Knowledge of average velocity calculations
  • Concept of area under a curve in physics
NEXT STEPS
  • Study the implications of variable acceleration on average velocity
  • Explore different velocity functions and their graphical representations
  • Learn about calculus applications in determining areas under curves
  • Investigate real-world examples of motion with variable acceleration
USEFUL FOR

Students of physics, educators teaching kinematics, and anyone interested in the principles of motion and acceleration.

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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