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 comment by @CuriousOne above.

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.

The energy required to accelerate an object by a given velocity increment is independent of the initial velocity in the non-relativistic limit (where $E_k=\frac{1}{2}mv^2$ applies). You are perhaps getting confused with the relativistic case where your statement is correct as 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

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 comment by @CuriousOne above.