The antonyms for the phrase "stopping running" include a range of words and phrases that connote movement, activity, and forward momentum. These could include "starting to run," "continuing to run," "picking up speed," "accelerating," or "moving forward." Other words that connote motion and energy include "sprinting," "galloping," "racing," or "charging ahead." Essentially, any word that implies a lack of movement or the cessation of running could be seen as an antonym for "stopping running." This includes phrases like "coming to a halt," "slowing down," "easing up," or "tapering off." In contrast, words that suggest ongoing activity and motion are natural antonyms for the phrase.