Editing Talk:Speed (section)

== 4 times energy for doubled speed ==

I have a question,

Why when you double the velocity of an object, you quadruple its speed rather than doubling it?

Has it anything to do with E=mc2 wherein mass is converted into energy by the square of light?

I mean if you "put" kinetic energy into an object, will part of it become "potential mass" and the rest actually become kinetic energy? Is that what explains why you have to square the number of times you want to increment the velocity in order to know the energy/power required?

I've looked everywhere and no one seems to explain why you have to square the energy in order to increment the velocity


I think you are a bit confused.  When you double the velocity, you do double the speed in the direction traveled.  All speed is, is the magnitude of the velocity.  Therefore both forward 3 m/s and backwards 3 m/s have the velocities +3 m/s and -3 m/s, respectively.  They have the same speed, 3.  What gets quadrupled is the kinetic energy.  KE = (1/2)mv^2 where m is mass and v is velocity.  If we plug in 2v for v (i.e. doubling velocity), we get the new kinetic energy (1/2)m(2v)^2 = (1/2)(m)(2^2)v^2 = 2mv^2.  We see this is quadrupled since 4*(1/2)mv^2 = 2mv^2.  As for the other part of the question about the role of E=mc^2.  This equation comes from [[special relativity]] and tells us how much energy an object would have if all mass could be converted to energy.   This formula is only useful with other energy equations when an object is moving at a substantial fraction (at least 10%) the speed of light and thus is not relevant to everyday calculations of [[velocity]], [[speed]], [[momentum]], or [[energy]].[[User:Aohara1986|Aohara1986]] 06:42, 19 October 2007 (UTC)