Then again, that is a problem with any rocket propellant/fuel... you take a lot of fuel and then propel it away, giving you some acceleration... you know what, never mind... that was a little stupid of me... the fact that you threw away the whole asteroid at the end, means that you gained that much momentum for yourself, regardless of how fast you threw the powdered substance away. I'll still post this, just in case someone else who, like me, has forgotten all physics might start wondering the same thing.
I wonder though, how much nuclear fuel would one have to carry to generate that much thrust? because, essentially the asteroid only gives you enormous amount of propellant to use, not fuel... to carry the amount of nuclear fuel that can propel essentially the whole asteroid away can't be a trivial problem!
On the eighth day, God created FORTRAN.