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April 30th, 2015, 07:11 AM   #1
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Question Is v in kinetic energy formula speed or velocity?

I know that kinetic energy is a scalar quantity and thus only has a magnitude, so does this mean that v in (1/2)mv^2 is speed and not velocity?
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April 30th, 2015, 07:28 AM   #2
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It doesn't matter because the square of the velocity is actually a dot-product.

$\displaystyle KE = \frac{1}{2} m \vec{v}^2 = \frac{1}{2} m \vec{v} \cdot \vec{v} = \frac{1}{2} m \left|v\right|^2$

The vector notation is a little sloppy, but I hope you get the point.
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April 30th, 2015, 07:44 AM   #3
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As Benit says, the $v^2$ is $\vec{v}\cdot\vec{v} = \big||v|\big|^2$ which is the magnitude of the velocity squared or the dot product of the velocity with itself. Either way it's a scalar value with no direction.

In practical terms, yes it's the speed. This should make sense, because energy doesn't have a directional component either.
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