Acceleration/Velocity Relationship

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SUMMARY

The relationship between distance, velocity, and acceleration is defined through their mathematical expressions and graphical representations. In the discussed example, the average acceleration is 0.5 m/s², while the instantaneous acceleration at t=16s is -1 m/s². The confusion arises from comparing the magnitudes of these values; however, the average acceleration is not greater than the instantaneous acceleration when considering their directional values. Understanding these concepts as vectors is crucial, as direction significantly influences their comparative analysis.

PREREQUISITES
  • Understanding of basic physics concepts such as distance, velocity, and acceleration.
  • Familiarity with vector mathematics and how direction affects magnitude.
  • Knowledge of graph interpretation, specifically velocity-time graphs.
  • Ability to perform calculations involving derivatives, such as Δd/Δt and Δv/Δt.
NEXT STEPS
  • Study the principles of kinematics in physics, focusing on the equations of motion.
  • Learn how to interpret and analyze velocity-time graphs in detail.
  • Explore the concept of vectors in physics, including vector addition and subtraction.
  • Investigate the relationship between instantaneous and average rates of change in calculus.
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Students of physics, educators teaching kinematics, and anyone interested in understanding the dynamics of motion and the relationships between distance, velocity, and acceleration.

tascja
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i was wondering if someone could explain the relationship between distance/velocity/acceleration? I don't have a clear understanding how they are related.. especially when they are plotted on a graph.

Ill give you a specific example:
so there was a velocity-time graph where the average acceleration (slope) over the entire graph was 0.5m/s^2. The instantaneous acceleration at t=16s was -1m/s^2. And it asked if the average acceleration was greater than the instantaneous or was the instantaneous greater than the average?
My thoughts were that since the instantaneous acceleration was greater in magnitude it was greater... this was wrong :( but i don't understand how or why??
 
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Velocity is the Δd/Δt. It is the time rate of change of displacement.

Acceleration the is the Δv/Δt = Δ (Δd/Δt) /Δt or Δ2d/Δt2

Both of these are vectors - and direction matters just like the displacement vector d that they are expressions of. You should view them as a continuum.

Hence -1 is greater than -2 but less than .5.
 

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