Let's choose an INTERVAL. We will look at one interval before and one interval after the time you chose so that we can find the average velocity.
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As the interval gets smaller, the line gets closer and closer to being a TANGENT line. And the average velocity gets closer and closer to being the instantaneous velocity.
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The slope on an x-t graph is the velocity. So the tangent line is showing us the slope at that point. We can get close to the tangent line using the average velocity idea.
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To think about: Why doesn't this work anymore if you set the interval to 0?
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To think about: Try changing the graph shape. What about a parabola? What about a sinusoidal graph? Or some other function that you know?
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This folder contains the calculations for making a line using the interval you chose. Look at how I did it if you'd like! :)
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