Some characters use their super-movement directly as an attack - teleporting people to great heights and then dropping them, or running into someone or punching them at very high speed.
The goal of the GM, and the player(s) in question, is to have an answer for the question "how would this power be opposed?", and/or "what is the real goal I have when using this power?"
An example of the former: a speedster's attacks can be countered by damaging zones of energy, slick surfaces, especially tough armor, and so forth. An example of the latter: a teleporter taking out a series of henchmen to sneak into a government complex isn't trying to kill them as his main goal, and failure doesn't mean the henchman survives. Instead, his real goal is to remove opposition and keep an alarm from being raised. In that case, a simple success at Overcome neutralizes the guards, while failure triggers the alarm.