183_notes:graphing_motion

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183_notes:graphing_motion [2021/01/24 00:11] – [Tracking the motion of objects] stumptyl183_notes:graphing_motion [2021/09/06 14:41] (current) – caballero
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 ===== Graphing Motion ===== ===== Graphing Motion =====
  
-//Predicting or explaining motion often requires you to use some sort of representation (or visual aid).// A common (and incredibly useful) one is the graph. In these notes, you read about graphs of motion and how to translate between different graphs. +Predicting or explaining motion often requires you to use some sort of representation (or visual aid). A common (and incredibly useful) one is the graph. **In these notes, you read about graphs of motion and how to translate between different graphs. 
 +**
 /* Write a constant velocity example graph position, talk about slope, graph velocity, talk about area; allude to acceleration */ /* Write a constant velocity example graph position, talk about slope, graph velocity, talk about area; allude to acceleration */
  
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 While the motion of the car, in principle, can occur 3 dimensions, it's not possible to represent all three dimensions and the time variable on a single 2-D graph. So, we have to select a component of the car's position (or velocity) to plot. In this case, let's assume the car moves to the right (i.e., in the +x direction). Perhaps, the plot of the car's position vs time looks like this: While the motion of the car, in principle, can occur 3 dimensions, it's not possible to represent all three dimensions and the time variable on a single 2-D graph. So, we have to select a component of the car's position (or velocity) to plot. In this case, let's assume the car moves to the right (i.e., in the +x direction). Perhaps, the plot of the car's position vs time looks like this:
  
-{{url>https://plot.ly/~PERLatMSU/10/640/480 640px,480px | Constant velocity (position vs time)}}+{{url>https://chart-studio.plotly.com/~PERLatMSU/10/graph-of-x-position-vs-time-for-a-car-moving-with-constant-velocity/#plot 640px,480px}}
  
 Here, you can see that the position of the car changes linearly with time, as we would predict for a car moving at constant velocity. From this graph, you can also determine the car's initial position (12 m), final position (132 m), and average velocity (12 m/s). Here, you can see that the position of the car changes linearly with time, as we would predict for a car moving at constant velocity. From this graph, you can also determine the car's initial position (12 m), final position (132 m), and average velocity (12 m/s).
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 For position versus time graphs where the position does not change linearly, you might need to determine (by taking the derivative) or approximate (by measuring very close points) the instantaneous velocity to model or explain the motion. For example in the graph below, a car moves to the right under [[:183_notes:constantf|constant force]]. Here, the slope (and thus, the velocity) changes at a constant rate and the average and instantaneous velocities are not the same. For position versus time graphs where the position does not change linearly, you might need to determine (by taking the derivative) or approximate (by measuring very close points) the instantaneous velocity to model or explain the motion. For example in the graph below, a car moves to the right under [[:183_notes:constantf|constant force]]. Here, the slope (and thus, the velocity) changes at a constant rate and the average and instantaneous velocities are not the same.
  
-{{url>https://plot.ly/~PERLatMSU/15/640/480 640px,480px | Constant force (position vs time)}}+{{url>https://chart-studio.plotly.com/~PERLatMSU/15.embed 640px,480px}}
  
  
-=== The area under the velocity vs time graph is the displacement ===+=== The Area Under The Velocity vs Time Graph is the Displacement === 
 + 
 +\\
  
 Sometimes, you will want to graph the velocity of the object as a function of time. Again, you have to graph a single component at a time. So, let's go back to the example of a car moving with constant velocity. In that case, we'd expect the velocity vs time graph to be a flat line taking on the value of the slope. In the graph below, we find that is the case. Sometimes, you will want to graph the velocity of the object as a function of time. Again, you have to graph a single component at a time. So, let's go back to the example of a car moving with constant velocity. In that case, we'd expect the velocity vs time graph to be a flat line taking on the value of the slope. In the graph below, we find that is the case.
  
-{{url>https://plot.ly/~PERLatMSU/14/640/480 640px,480px | Constant Velocity (velocity vs time)}}+{{url>https://chart-studio.plotly.com/~PERLatMSU/15.embed 640px,480px}} 
 + 
 +/*{{url>https://chart-studio.plotly.com/~PERLatMSU/15.embed 640px,480px | Constant Velocity (velocity vs time)}}*/
  
 In addition, we can use the position update formula to show that the x-displacement ($\Delta x$) is the area under this curve: In addition, we can use the position update formula to show that the x-displacement ($\Delta x$) is the area under this curve:
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