🚀 go-pugleaf

>	 As we approach c, the graph has begun to approach the vertical
> asymptote.  More and more, our Kinetic energy (remember, KE=(mv^2)/2)
> is increasing the mass, rather than the velocity.  We can add KE to
> our heart's content;  The universe won't care, we'll continue to
> travel along that hyperbolic line, approaching v=c, but never quit
> obtaining it.

You're mixing frames.

If you're the thing which is accelerating, everything is wonderful,
as long as you have the reaction mass, you'll continue to accelerate
to your heart's content.  Your mass will measure the same (to you), it's
just as easy to accelerate now as it did  when your journey started,
assuming :-) no particles in your path and the speed of light police
don't get you :-).

If you're accelerating something, then you will see that it takes more
and more energy to get the thing to go faster, kinetic energy goes up,
but some of the energy goes into mass.  The velocity
of that object will travel along that hyperbolic line.