The warp 2 barrier was a warp barrier.
It was the limit of warp speed in the preliminary stages of warp technology (21st and 22nd centuries). It was not until the 2140s that a warp engine conceived at the Warp Five Complex by Henry Archer broke this barrier. Commanders A.G. Robinson and Jonathan Archer demonstrated this advanced warp engine in the second Template:ShipClass prototype, the NX-Beta. (ENT: "First Flight")