Going from position vs. time to velocity vs. time

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SUMMARY

The discussion focuses on converting position vs. time graphs to velocity vs. time graphs, emphasizing the importance of accurately interpreting the initial conditions and the nature of acceleration. Participants noted that the original position-time graphs do not exhibit parabolic shapes, indicating that the velocity-time graphs should feature curved lines rather than straight ones. The conversation highlights the necessity of understanding the actual velocity at time zero and subsequent moments to create accurate velocity-time representations.

PREREQUISITES
  • Understanding of kinematics, specifically position vs. time and velocity vs. time graphs.
  • Familiarity with the concept of acceleration and its implications on graph shapes.
  • Basic skills in interpreting graphical data and making estimations based on visual information.
  • Knowledge of calculus fundamentals, particularly regarding curves and rates of change.
NEXT STEPS
  • Research the principles of kinematics to deepen understanding of motion graphs.
  • Study the effects of constant vs. variable acceleration on graph shapes.
  • Learn how to derive velocity from position-time graphs using calculus.
  • Explore graphical analysis techniques for accurately sketching velocity vs. time graphs.
USEFUL FOR

Students and educators in physics, particularly those studying motion and graph interpretation, as well as anyone involved in teaching or learning about kinematics and graphing techniques.

Kelly k
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I attached the info that I need help with I am really struggling and the lines that are drawn in red are my guesses. PLEASE HELP!
 

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This is a bit tricky. Your answers are sort of right, but you have assumed constant accelerations (that is, you have drawn straight lines). I see no such statement in the question. Indeed, the position-time graphs don't look like parabolas, suggesting the v-t graph should have curved lines. As against that, drawing accurate curves is going to be hard without a lot of detailed measurement of the given curves.

So let's pretend acceleration is supposed to be constant.
Your first graph is fine, except that you need to think about the actual velocity at time 0. What would you say that is, looking at the position-time graph?
2nd graph is ok.
For the third, what is the velocity at time 0? What is the velocity a bit later?
 

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