Here's an example of a photographer using a slow shutter speed with a pan to create a sense of fast movement during a swimming competition. Their faces are only out of the water for a split second so your timing has to be just right, or you end up with something like the woman at the bottom of this frame.

Martin Bureau/AFP - Getty Images
US swimmer Allison Schmitt (top) and Great Britain's Joanne Jackson compete during the women's 200m freestyle swimming heat at the National Aquatics Center in Beijing at the Olympic Games on August 11, 2008.