To accelerate something, you interact with it.
We know about four interactions, weak, strong, EM, and gravity.
EM is convenient, because it's a long-distance force (carrier of the interaction is massless).
Gravity also works, for the same reason, but it's weaker. You could put a neutron at the top of a very tall tower and it will accelerate towards the ground.
Weak and strong forces are short-distance. Weak is short-distance because it's carriers are very heavy, and strong is short-distance because there are no free gluons and you need heavy particles (e.g. virtual pions) to mediate the interaction. You need a long-distance force accelerate a particle in the vacuum far from any other objects.
That does not mean that you can't use weak and strong interactions at all. You could create a cloud of neutrons and fire a beam of protons at it. Some protons will scatter on neutrons and pass momentum on to them.