During the second year of life, the rate at which children acquire new words accelerates dramatically. This has led the field of language acquisition to posit specialized mechanisms that leverage the few words learned in the initial slow phase for faster vocabulary growth later. Simulations and mathematical analysis demonstrate that specialized cognitive changes are unnecessary. The acceleration in lexical acquisition is a necessary by-product of learning if (i) multiple words are learned in parallel and (ii) words are distributed such that there are few words that can be acquired quickly and many difficult ones.