When it comes to describing an increase in speed, there are plenty of ways to vary your language. For "quickened one's speed," you might say you hastened, hurried, or hastened your steps. Alternatively, you might describe your movement as becoming swift, expeditious, or fleet-footed. Another option is to describe your upping the pace by saying you picked up the pace, increased your tempo, or boosted your momentum. Whether you're in a hurry to catch a train or racing to the end of a race, the words you use to describe your increased speed can add flair to your language.
