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If the mass remained constant and you continuously applied a small force for a very long time, the object would attain very high speeds. Unfortunately, the mass increases exponentially, so you have to keep increasing the force exponentially to maintain the acceleration. Pretty soon you've used up more energy that the Universe contains to maintain the acceleration.

(That's an an approximation - no doubt some smartypants will point out some serious flaws in my description.)

What a challenge! -- all right I will be the smartypants.

The increases in mass and required force are asymptotic, not exponential.

With an exponential increase, any resulting velocity

*v* could be achieved with a finite input of

*a*^{v}An asymptotic increase is worse, because the force increases as

*ac/√(c*^{2} − v^{2}), which becomes infinitely large as

*v* approaches

*c*, and meaningless if

*v* exceeds

*c*