My Math Forum Is v in kinetic energy formula speed or velocity?

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 April 30th, 2015, 07:11 AM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus 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?
 April 30th, 2015, 07:28 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,111 Thanks: 706 Math Focus: Physics, mathematical modelling, numerical and computational solutions 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. Thanks from Mr Davis 97
 April 30th, 2015, 07:44 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 Math Focus: Mainly analysis and algebra 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. Thanks from Mr Davis 97

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