Surely the speed of the impacting mass would be increased by orders of magnitude if it contained in its centre a nuke that exploded at the moment of impact.
The idea you are pursuing here - finding ways to convert the radiation energy released by a thermonuclear weapon into kinetic energy to generate effects in space - has fortunately already been studied by NASA! It's called the Casaba Howitzer. In effect, it is a nuclear shaped charge that efficiently converts a bomb's radiation energy into kinetic energy, specifically, a blast of tungsten plasma. For obvious reasons it is a popular warhead choice in science fiction.
Even better, the howitzer's effects can be tuned; by modifying the design one can adjust the angle (and thus the destructive effects) of the directed plasma "beam." This is because the howitzer was originally intended for use with Orion pusher-plate spacecraft - it wasn't until the scientists said "now we must be very careful with our figures lest we focus the plasma too much and blast clean through the massive monolithic steel pusher-plate" that they realized what they had just done.
Even without deploying a Casaba Howitzer device, nukes have plenty of utility in deflecting asteroids, even so-called "rubble pile" asteroids that seem to be very common. A close-range detonation (some tens or hundreds of meters, depending on the yield and the size of the rock) will efficiently bake and/or vaporize the dust and smaller debris, thus generating thrust (and the radiation of thermal energy will also alter the rock's orbit; an accelerated version of the Yarkovsky effect which is what causes these rocks to wander into occasional earth-crossing orbits to begin with. Due to how orbital mechanics works, a very small nudge applied far enough in advance can make the rock miss Earth (which is a very small target in a very big solar system.) However, given the state of our sky searches, we may only find a rock some months or even weeks before impact, in which case we would want to compensate with a much bigger nudge - and lord knows we have enough thermonuclear assemblies between all the nations of earth to provide it. :)