What does the slope of a velocity vs time squared graph represent?

AI Thread Summary
The slope of a velocity vs. time squared graph represents the relationship between velocity and the square of time, indicating how velocity changes with time. It is suggested that the slope of the distance vs. time squared graph is half of the acceleration, highlighting a connection between these variables. The discussion emphasizes the importance of understanding these relationships in kinematics. Clarification on how these slopes relate to acceleration and the rate of change of acceleration is sought. Overall, the thread explores the mathematical implications of these graphs in physics.
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Basing on the units, the velocity vs time is equal to acceleration. What about the velocity vs time squared and distance vs time squared graph?

Is the slope of the distance vs time squared graph one half of the acceleration? If it does, please explain.. :)
 
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Rate of change of acceleration and acceleration respectively.
 
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