Kinetic Energy and Momentum Scalar

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bravoghost
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This is a conceptual problem that I'm sure is pretty common. How can kinetic energy (1/2mv^2) be a scalar quantity when it includes a vector quantity like velocity?
 
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v^2 can be written as the dot product v*v, and a dot product is a scalar.
 
Because, as Svalbard stated, the square of a vector is a scalar.
 

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