Enterprise Exceeds Warp Limits

 

The Enterprise is able to only achieve Warp 9.5 "with extreme risk" (Encounter at Farpoint). However, there have been various times when this 'speed limit' has been exceeded.

 "Where No One Has Gone Before" - In a warp field experiment with the Traveler, Wesley's distraction causes the Traveler to phase in and out, and causes the Enterprise to travel 2.7 million light years in a few seconds.

 "When The Bough Breaks" - When Captain Picard insists that the Aldean people return the children kidnapped from the Enterprise, the Enterprise is hit with a bolt of energy that causes it to travel such a distance that it would take three days to travel back to Aldea at Warp 9.

 Q Who" - Q, with the snap of his fingers, send the Enterprise 7,000 light years away for their first encounter with the Borg. Also, when the Enterprise is being chased by the Borg, LaForge reads the speed off as Warp 9.65.

 "Legacy" - In the teaser, the Enterprise is going Warp 9.6 to Tasha Yar's birthplace.

 The Nth Degree" - Barclay, with the knowledge gained from an alien probe, creates a space distortion that causes the Enterprise to travel halfway across the Galaxy.

 "Descent" - The Enterprise uses a transwarp conduit while chasing the Borg and tracking down Data.

 

The law on starship engines: there are never odd numbers of engine nacelles on starships (from Gene). Rationalization (from the `Technical Advisors'): it has something to do with Warp Field geometries...