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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: 2,099 Thanks: 703 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
It doesn't matter because the square of the velocity is actually a dotproduct. $\displaystyle KE = \frac{1}{2} m \vec{v}^2 = \frac{1}{2} m \vec{v} \cdot \vec{v} = \frac{1}{2} m \leftv\right^2$ The vector notation is a little sloppy, but I hope you get the point. 
April 30th, 2015, 07:44 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,274 Thanks: 2435 Math Focus: Mainly analysis and algebra 
As Benit says, the $v^2$ is $\vec{v}\cdot\vec{v} = \bigv\big^2$ 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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energy, formula, kinetic, speed, velocity 
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