Representing instantaneous velocity vs time on a graph

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SUMMARY

The discussion centers on creating an instantaneous velocity vs time graph for an object moving at a constant velocity. The key equation involved is v = dx/dt, where v represents instantaneous velocity in meters/seconds. The graph should depict a horizontal line, indicating that the velocity remains constant over time. The confusion arises from the need to represent displacement in terms of velocity, but the correct approach is to maintain the standard representation of velocity as a function of time.

PREREQUISITES
  • Understanding of calculus, specifically derivatives
  • Familiarity with the concepts of velocity and displacement
  • Basic graphing skills for plotting functions
  • Knowledge of units of measurement in physics, particularly meters/seconds
NEXT STEPS
  • Study the concept of derivatives in calculus, focusing on their application in physics
  • Learn how to graph linear functions, particularly constant functions
  • Explore the relationship between position, velocity, and acceleration in kinematics
  • Review examples of instantaneous velocity graphs for different types of motion
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and graphing motion, as well as educators seeking to clarify the concepts of instantaneous velocity and its graphical representation.

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Homework Statement



I need to draw an instantaneous velocity vs time graph of an object moving at a constant velocity, provide an equation, and explain what it all means. I know that instantaneous velocity is typically shown as dx/dt (the derivative of change in position with respect to time and I know the unit of measurement would be meters/seconds) However, because it says to show velocity, I feel like I need to represent the displacement in terms of v instead of x yet in going online to see how it's shown, it had looked like v was the typical variable used. I also have to draw one for position vs time (average velocity) so I'm not sure the best to show it for the instantaeous velocity graph as I know velocity is typically shown when representing acceleration. Any input would be appreciated!
 
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I need to draw an instantaneous velocity vs time graph of an object moving at a constant velocity, provide an equation, and explain what it all means. I know that instantaneous velocity is typically shown as dx/dt (the derivative of change in position with respect to time and I know the unit of measurement would be meters/seconds) However, because it says to show velocity, I feel like I need to represent the displacement in terms of v instead of x

You might be over thinking the problem. The question says..

I need to draw an instantaneous velocity vs time graph of an object moving at a constant velocity

How do you show

y(t)=constant

on a graph of y vs t?
 

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