Motion: Feynman's Physics Explained
The world is always changing — how do we describe change precisely? The ancient Greeks tied themselves in knots over this. The answer required a new branch of mathematics: calculus. If a car is speeding up, what is its speed right now? Look at the tiny distance it covers in a tiny interval of time and take the ratio. Calculus is the machinery for doing this rigorously. It was not an abstract game — it was invented as the natural language for the physics of motion.
The big idea
Calculus is the language for describing things that change.
Think about it
What is the difference between your average speed on a trip and your speed at one exact instant?
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