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A ball is thrown straight up and returns to the same point. The book says displacement is zero but distance is not. How can that be?
Distance is the total length of the actual path travelled, so it only adds up and can never decrease. Displacement is the straight-line vector from the starting point to the final point, with direction, and it only cares about where you start and end, not the path. When a ball is thrown straight up, say to a height h, and returns to the launch point, the path it covered is h going up plus h coming down, so the distance is 2h. But the final position is exactly the starting position, so the displacement is zero. This is why distance is a scalar that keeps growing while displacement is a vector that can be zero even after a long journey. The same idea applies to round trips in any direction.
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