Uniform Acceleration: Why (v+v0)/2 Works

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SUMMARY

The formula (v + v0)/2 accurately calculates the average velocity only under conditions of constant acceleration. This is due to uniform acceleration resulting in a linear relationship between velocity and time, allowing for evenly distributed displacement. In scenarios where acceleration varies, such as a car accelerating from 0 mph to 100 mph and then decelerating, the formula fails to represent the average accurately without segmenting the motion into distinct phases. The discussion emphasizes the importance of understanding kinematic equations and their limitations in real-world applications.

PREREQUISITES
  • Understanding of basic kinematic equations
  • Familiarity with concepts of velocity and acceleration
  • Knowledge of uniform versus non-uniform acceleration
  • Ability to perform basic arithmetic operations for averages
NEXT STEPS
  • Study the derivation of kinematic equations in physics
  • Learn about the concept of instantaneous velocity versus average velocity
  • Explore real-world examples of non-uniform acceleration
  • Investigate graphical representations of motion and acceleration
USEFUL FOR

Students of physics, educators teaching kinematics, and anyone interested in understanding motion dynamics and the application of kinematic equations in real-life scenarios.

Omar.Castillo
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hey guys will you help me out or give me links to understand why the formula (v + v0)/2 works out only when acceleration is constant? I believe it has to do with uniform acceleration maintaining an evenly distributed displacement, but I need to get this right so I can understand it clearly
 
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It's an even change of velocity with respect to time. Let's say that I was driving my car, and went from 0 mph to 100 mph in 60 seconds, but then slowed down to 45 mph for 3 hours. That formula wouldn't show me an average acceleration over the entire time would it? I'd have to break it down into smaller parts. Also, most things do not accelerate uniformly, that is they speed up faster and slower all the time. It's hard to find things that fit the ideal conditions of the kinematic equations. That is why that formula produces the average acceleration.
 
please find average of 2, 4, 6, 8, 10
and of 2, 4, 5, 6, 10
 

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