we know long enough in advance that they are on an impact trajectory. Deflecting them is not difficult for modern technology. Detecting them IN TIME IS difficult. A ten megatonne warhead weighs only a few tonnes (six megatons of TNT per metric tonne of bomb), about the same as a great many interplanetary probes. An impact burst would blast off enough matter to deflect the course of a 10 km asteroid by a good fraction of a meter per second. A year contains 30,154,000 seconds. So even a fifth of a meter per second delta-V (easily obtainable) would alter the trajectory by 6,000,000 meters in a year. Since the Earth's radius = 6,300,000 meters, this is about the radius of the Earth, sufficient deflection to turn a direct hit into a near miss, provided that we hit it a year before impact. Two years is much better. But one week's notice is worthless. We must keep our eyes open and devote sufficient resources to determine the trajectory with great accuracy sufficiently long in advance. There is NO ROOM FOR ERROR in this affair. If we blunder, we could turn a near miss into a direct hit. There are three unknown critical parameters:
Mass of impactor
Trajectory of impactor
Delta-V caused by contact burst

DFM