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From the equation $E_k=\frac12mv^2$ you can determine more energy is necessary to accelerate a mass the higher your initial velocity is. For example, three times more energy is necessary to accelerate a mass from 1 m/s to 2 m/s than from 0 m/s to 1 m/s. If the earth is moving in the universe, what is our standard frame of reference? Why?

Thanks in advance for your time and answers

DanielSank
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J Physics FM
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    See https://physics.stackexchange.com/questions/535/why-does-kinetic-energy-increase-quadratically-not-linearly-with-speed?rq=1 for understanding this... – navigator Jan 26 '16 at 13:55
  • The Earth is not moving "in the universe", but relative to other bodies in the universe. Kinetic energy is observer dependent and different observers would need different amounts of energy to accelerate the same body by the same amount relative to their inertial systems. – CuriousOne Jan 26 '16 at 16:29

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The energy required to accelerate an object by a given velocity increment is linear in the initial velocity in the non-relativistic limit (where $E_k=\frac{1}{2}mv^2$ applies). It is even more energy intensive for the relativistic case when the velocity of light (c) is approached. That is because the relativistic expression for kinetic energy is: $$E_k=mc^2(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1)$$.

Here is a site that should clarify both the relativistic and non-relativistic cases if you make use of the available links. http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html For your last question see the comments by @CuriousOne and @navigator above.

Lewis Miller
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