Imagine a crab scuttling around a beach, leaving a trail in the sand as it goes. There are several questions we might ask about the crab's motion.
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At any time, which direction is the crab moving in?
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How fast is the crab moving?
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How much does the crab change its height as it, say, climbs up a sandcastle?
We'll learn to answer these questions by studying motion along a path.