How can I conduct an experiment to show that the area under a velocity-time graph equals the displacement when the velocity is changing at a constant rate? I've tried to measure free falling objects, but I realized that it's hard to measure free falling objects at home.

And does this online simulation (https://www.geogebra.org/m/UDUdnA32) replicate real life?

  • $\begingroup$ What do you mean by your last sentence? $\endgroup$ – noah Jul 8 at 21:45
  • $\begingroup$ If I was to conduct an experiment like the one in the simulation, would I get the same result? $\endgroup$ – Austin Gae Jul 8 at 21:55
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    $\begingroup$ If you manage to start at a controlled initial velocity and maintain a constant acceleration, then yes. But in experiments it is always vital to do error analysis. $\endgroup$ – noah Jul 8 at 22:10
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    $\begingroup$ You can try something similar to what Galileo did: use an inclined plane, so acceleration is reduced to something manageable. $\endgroup$ – hdhondt Jul 8 at 22:59
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    $\begingroup$ What do you think you are testing? I ask because the typical way of thinking about this defines velocity such that the area under the curve is equal to the displacement. It is a mathematical truism because we define it to be true. It may help to separate the thing you wish to test from this definition, so that you can better focus on the part you wish to actually test. $\endgroup$ – Cort Ammon Jul 9 at 0:04

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