Curiously, characters with Super Speed tend to also have super acceleration and deceleration: they usually reach their regular running speed instantly and are able to stop on a dime without harm.
You only see them "speeding up" if they're trying to reach some extreme level of speed they usually aren't accustomed to.
(Unfortunately, the speed factor is usually forgotten, and time is treated as if it really did just stop.) A (slightly) less egregious option is simply to have the speedster move so fast that he appears to duplicate himself - appearing in two places with so little real time passing in between that the brains/sensory equipment of any observers see him in two places at once.
Speculative Fiction writers love to apply this trope to the Theory of Relativity, The Theme Park Version of which says, "If you go fast enough, you'll alter the flow of time, and you can Time Travel to the future or the past." Characters who can't travel through time get the opposite effect: They can speed up so fast, it's as if time stops for the rest of the world.
"Keystone City has become a utopia— a protectorate relentlessly patrolled by a gale force once human. A typical trick speedsters can do is run up the side of a building and even across a body of water.
Extremely skillful speeders are capable of creating multiple "light clones" in this fashion.
Speed dating may sound silly to some, but in fact, it can be a successful way to meet new people and garner prospective dates.