(Kindly read the details before answering) How much energy would be actually required for a 1 kg object to reach the speed of light in a vacuum?

Infinite. Full stop. Sorry, do not pass Go, do not collect $200.

i understand everyone says its infinite. But the details i presented seem to give the solution. Can you please point out the flaw?

http://en.wikipedia.org/wiki/Relativistic_rocket

Rockets (except for the purely theoretical photon rocket) do not work by converting fuel into energy into kinetic energy, so E=mc^2 doesn’t apply here. And if it did, the m you use is rest mass.

but A’s frame of reference isn’t m going to be 1 kg and therefore energy required to accelerate it be constant for every increment too? and hence, the mass of fuel required will also remain the same for every increment?

wouldn’t it be infinite for us earthly observers only?

Well, from the point of view of passengers onboard the spacecraft, you can theoretically go as fast as you want as the universe Lorentz-contracts in the direction of travel.

See also: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

@hiphiphopflipflapflop thanks, i appreciate your response :)

Why not ask for 99.99% light speed for a one kg object?

It can only be infinite, as you approach c, the mass of the object will approach infinity. It does not really matter if you start with 1t, 1kg or 1g. Any object with mass travelling at c will have infinite mass, to accelerate it to c will thus require infinite energy.

I do wonder though if we could do it if we reduced to object’s mass to absolute 0.

@ragingloli What is your take on the argument presented in the detail of the question? Why aren’t we considering the fact that in the frame of reference of the object A, its mass remains constant no matter what speed it is moving at?

Also, you are assuming that the increase in mass with increase in velocity is only true for an outside observer, which I do not think is true.

Well, you know about Time Dilation- if i am moving fast, my clock will appear to be ticking slowly to you if you are at rest or at low speeds. But for me, my clock will be ticking normally!
Similarly, my mass will be larger to you, but it will remain normal from my point of view. I believe that’s stated clearly in the theory of relativity.

@krrazypassions, it’s easier to understand the content of Special Relativity in the context of time and length dilation; i.e., that you will “appear” infinitely short or “seem” to take x amount of time to travel. But the increase in mass is a real event. The information you need is here. Essentially, relativity makes a number of claims about the substance of the universe and the behavior of spacetime. Time and length dilation and the mass increase are all consequences of this.