You'd need to know in advance that the Kinetic Energy and Work equations are scalars. Anyways, I drew this to demonstrate that KE can still be written in terms of velocity (and not speed) v. 

I was reading some physics stuff today, and I saw that in the Kinetic Energy Equation (KE = 0.5mv^2), v is used, but v represents speed instead of velocity. I understand why Kinetic Energy is related to speed and not merely velocity, but why is v used to represent it? v represents velocity in many other equations. It seems really screwed up because there is already common confusion about the difference between speed and velocity. Also, is there any other symbol for speed itself in physics? I know that c represents the speed of light, but I am talking about just general speed. 

You'd need to know in advance that the Kinetic Energy and Work equations are scalars. Anyways, I drew this to demonstrate that KE can still be written in terms of velocity (and not speed) v. 

Because a vector to the second power yields a scalar, so it doesn't matter if you use speed or a velocity. And v is a common symbol. 

April Ryan is my friend,
Every sorrow she can mend.
When i visit her dark realm,
Does it simply overwhelm.
My God, now I know how this guy feels. 

Your equation is incomplete 

Last edited by ninja9578; 02272010 at 02:35 AM.
WTF? 

c is the speed of light. 

Last edited by ninja9578; 02272010 at 03:06 AM.
Oh, no. Imagine that you have a velocity V (which I called V subc in the image) at whatever angle. That velocity has both an x and y component, which I labeled Vb and Va respectively. You can apply the Pythagorean theorem (a^2 + b^2 = c^2) to these two components to get that resultant vector V. I only brought it up in order to demonstrate that taking the dot product of V with itself equals the same thing, and through that you can represent speed in terms of velocity in the KE equation. V dot product itself is equal to speed squared, or the magnitude of V squared. 

I am aware of the foot note, but that is the equation I am asking about. It is called the Kinetic Energy Equation. It is the subject of this thread. I am not concerned with speeds that are substantial fractions of the speed of light in this thread. 

Magnitude also strips direction. Absolute value has a direction in the positive direction, magnitude doesn't. Weird little technicalities are what so frustrates high school physics students and stoners. I will get so into this thread in a little bit. 

200m north how? 

Last edited by Invader; 02272010 at 04:37 AM.
"Low speeds"... I wouldn't call speeds up to 0.1 * c to be "low" :p 

Last edited by khh; 02272010 at 04:37 AM.
April Ryan is my friend,
Every sorrow she can mend.
When i visit her dark realm,
Does it simply overwhelm.
Velocity is a vector and so should technically be written in bold as v or underlined as v. It has (3 in our universe) dimensions. 

Last edited by Xei; 02272010 at 03:16 PM.
Hm... I believe you, but I don't think I saw v or v used to represent velocity in any of the stuff I read. I was of course talking about a zig zag path involving friction, air resistance, or other counterforce. I am not trying to get into a discussion about that zillions of potential factors that could affect motion. I am just curious about what the v in the equation represents and why v, of all variables, would be used to represent speed. 

My point about the zig zag is that you have to realise that kinetic energy and drag forces are two utterly different concepts. Once you put energy into an object so as to give it KE, travelling along a path, even if not a straight one, does not inherently alter the KE. 

Last edited by Xei; 02272010 at 06:55 PM.
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