Slope and Area Under the Curve: How Position, Velocity, and Acceleration Connect

Position, velocity, and acceleration aren't three separate topics, they're the same motion read off three different graphs, and the slope/area relationship between them is the one idea that makes every motion graph problem solvable without calculus. This video builds that relationship from the ground up, algebra only. Covered in this video: Velocity is the slope of a position-time graph; acceleration is the slope of a velocity-time graph Displacement is the area under a velocity-time graph; velocity (change) is the area under an acceleration-time graph Why this works without calculus: rise over run and base times height carry the whole idea at this level The signed area rule: when a velocity-time graph dips below the x-axis, that area counts as negative displacement, and why that actually makes physical sense (the object is moving backward) Working an example where positive and negative areas partially cancel, so total displacement is smaller than total distance traveled How to read all three graphs (position, velocity, acceleration) together and know which one to check first depending on what the question asks This is the backbone of Standard 2.2 (Kinematics and Motion Graphs). Once slope and signed area click here, the rest of the unit is just applying this same idea to harder graphs. AUX — Free Physics Resources https://auxlearning.com