<As an object accelerates, it's mass increases.

It's my understanding that this concept is out of favor at the time being due to problematic implications. As my advisor said in a class he was teaching, avoid "it" like the plague.

The more favorable notion is that the relativistic kinetic energy or momentum (depending on what you care about, some say momenergy) increases in the same proportion as before, just without the increasing mass.

Therefore, as the object approaches the speed of light, it's energy approaches infinite. Therefore, the amount of energy required to accelerate it also approaches infinite. The end result is that the object would approach but never quite equal the speed of light.

This is all still good though..... ;)