Stewart 8e 13.4.19 minimize the 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIidGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJ0RidGL0YyRjk=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Notice that the velocity is a straight line in velocity space, so answering this question (when is its length minimum) is equivalent to finding out where the line is closest to the origin.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 we plot this function, the minimum is obvious, at the vertex of the parabola.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