Velocity is a one-on-one competitive sport that seems to be a cross between handball and a phaser range. Each player must avoid being hit by a disk by shooting it and sending it back toward their opponent. It is fast-paced game of wit and physical endurance, with both players in constant motion.
The disk that is used in the sport is an aerodynamic, metallic object, eight inches across, glowing different colors when hit by each competitor's hand phaser. Velocity is played in rounds, and is concluded when one of the players achieves a "full impact" of the disk with his or her opponent's body.
Velocity was first introduced in canon in the Voyager episode "Hope and Fear," when Captain Janeway and Seven of Nine played a game of Velocity in the holodeck. Janeway won the game, surprising Seven, who thought she should have been able to win due to her biological enhancements. Janeway tells her that there is more to the game than stamina - intuition is a critical part of the game.