How to calculate motion by finding the area under a curve
In short: Learn how calculus reveals an object's movement. By integrating acceleration or velocity over time, you can determine exactly how much an object's speed or position has changed, visualized as the area under a graph.
In physics, motion is not just about instantaneous values but the accumulation of change. The change in an object's velocity over a specific interval is found by calculating the integral of its acceleration with respect to time. Graphically, this corresponds to the signed area between the acceleration curve and the time axis.
Similarly, displacement—the total change in position—is the integral of velocity over time. Just as with acceleration, this value is represented by the signed area between the velocity curve and the time axis. Understanding these relationships allows you to derive complex motion patterns from simple graphical representations.
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Sources
- Summary by Intellect · source: Kinematic quantities: Accumulations of change | AP Physics | Khan Academy
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