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| 183_notes:graphing_motion [2025/11/12 21:12] – hallstein | 183_notes:graphing_motion [2025/11/12 21:20] (current) – hallstein |
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| This is precisely how one defines a [[http://en.wikipedia.org/wiki/Riemann_sum|Riemann sum]] to determine the area under a function. This area is highlighted in light blue, and is precisely equal to the difference in the initial and final position in the first graph (120 m). The car travels at 12 m/s for 10 s. Notice the displacement is positive because the area under the curve is measured from the function to y=0. | This is precisely how one defines a [[http://en.wikipedia.org/wiki/Riemann_sum|Riemann sum]] to determine the area under a function. This area is highlighted in light blue, and is precisely equal to the difference in the initial and final position in the first graph (120 m). The car travels at 12 m/s for 10 s. Notice the displacement is positive because the area under the curve is measured from the function to y=0. |
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| For situations where the object does no move with constant velocity, the area under the velocity vs time graph is still the displacement, it just might be slightly more complicated to calculate. For example, here's the velocity vs time graph for when the car moves under a [[:183_notes:constantf|constant force]]. | For situations where the object does no move with constant velocity, the area under the velocity vs time graph is still the displacement, it just might be slightly more complicated to calculate. For example, the graph link here: [[https://msuperl.org/interactive/mechanics/CA_velocity_vs_time_area_fill.html|Constant force, velocity vs. time]] is the velocity vs time graph for when the car moves under a [[:183_notes:constantf|constant force]]. |
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| {{url>https://plot.ly/~PERLatMSU/16/640/480 640px,480px | Constant force (velocity vs time)}} | /*{{url>https://plot.ly/~PERLatMSU/16/640/480 640px,480px | Constant force (velocity vs time)}}*/ |
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| The triangular area (highlighted in light blue) under the curve is the displacement of the car in the x-direction. Notice it's positive because it's above the y-axis. "Area under the curve" actually refers the the area between the function and y=0. If the plot is below the y=0, then that part of the area is negative. | The triangular area (highlighted in light blue) under the curve is the displacement of the car in the x-direction. Notice it's positive because it's above the y-axis. "Area under the curve" actually refers the the area between the function and y=0. If the plot is below the y=0, then that part of the area is negative. |