If you're looking for synonyms for the phrase "quickened one speed," there are several options to choose from. For example, you could use the word hastened, which suggests a sense of urgency, or accelerated, which implies a deliberate effort to increase speed. Another option might be to use the word expedited, which suggests the act of making something happen more quickly than it would otherwise. Additionally, you could use the phrase increased one's pace or simply say that someone moved faster. Whatever word or phrase you choose, the goal is to convey a sense of urgency or purposeful action, indicating that someone is moving quickly and with intention.