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Is Star Trek 3000 years too advanced?

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Star Trek takes place in the 2200's and in the Star Trek Universe FTL (Faster than Light) speeds were developed in 2062. Star Trek in a Kardashev 2 type civilization. I personally think that light speed won't be possible until atleast 2492. Mankind is predicted to become a Kardashev 2 Civilization in the year 5,200 which is about 3000 years after Star Trek takes place. Is Star Trek being unreasonable about their technological feats, so early on? It doesn't seem possible for a civilization that has just discovered space travel to be able to travel Faster than the Speed of Light in only 54 years, or 2062. Star Trek should take place in the 5200's not the 2200's. Any comments or suggestions?