There are many words that can be used as synonyms for the phrase "become faster." Some common options include accelerate, quicken, hasten, speed up, expedite, and advance. These words all suggest an increase in speed or pace, and can be used in a variety of contexts. For example, you might say that a car accelerated quickly from a stop sign, or that a runner hastened their pace in the final stretch of a race. Whatever the situation, using these synonyms can add variety and interest to your writing, while also providing important information about the speed and intensity of the action.