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While you cannot physically square your velocity, such as you are traveling at 10 meters per second, and then there's another dimension where you are 100 meters squared per second squared, velocity squared comes up in various physics calculations. Kinetic energy of an object in motion is (1/2)*mass*(velocity squared). This just means that you take the velocity and square the number, and also square the units, so (10 m/s)2 = 100 m2 / s2 for the calculation.

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