I don't think you would try to slow down approaching meteorites to zero speed, only deflect them a little so that they miss the planet. The further away you catch it, the less energy it takes (I assume, didn't do the maths).
Debatable. On the one hand, the farther the projectile is from the planet, the less it needs to be deflected. On the other hand, you have to expend energy to get to the damn thing in the first place.
I suppose the survival of your species renders moot most energy concerns though.
It depends on the momentum of the asteroid. If I've accelerated an asteroid up to .5c, then even if you discover the attack years ahead of time you might still not have the energy to deflect the asteroid by enough to save your planet.
You also have to remember that the attacker can launch multiple simultaneous asteroids. You might have enough nukes to deflect one asteroid. Do you have enough to deflect ten? A hundred?
If you can accelerate an asteroid up to .5c, you have harnessed energy resources to power the earth for a gazillion years. You would be so rich that you dont need to be a warlord. You could become ... a banker.
Actually, at .5c from the Kuiper belt, the warning time is only 30 hours or so and the momentum is such that deflection is impossible. I'm too lazy to do the math but the collision would be spectacular.
Momentum doesn't really work this way. The only things that change the difficulty of deflecting something are it's mass, and the remaining time to impact.
Having a lot of momentum doesn't change how much force is required to give something a given acceleration until relativistic effects start to matter.
(I guess distance also makes it harder, because you need to travel further to start deflection, but that's not really a momentum thing)
