The question isn't really valid in this universe. But to give an answer, you will NOT reach light speed, not from your reference frame or from any other. Sorry friends

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Here is what would actually happen:

According to Earth's reference frame, your acceleration will continually decrease as you approach the speed of light. They will never see you reach the speed of light. They will, however, see your energy/momentum approach infinity.

According to the ship's frame, you are at rest (lol). You are eternally moving at zero speed. Of course, that isn't what we want to hear, and it goes to show how careful we must be about defining these things. Even more so when we're talking about relativistic situations.

Now for what we actually want to discuss: your acceleration and speed with respect to the world around you. We must take relativistic effects into account. For example, the distance in front of you will CONTRACT the faster you go with respect to those objects. This means that while you traveled, say, 5000 light years according to Earth, from YOUR frame of reference you might have only moved 5 meters (because, again, the distance in front of you contracts-btw to get that to happen, you'd have to have reached about 99.9999999999999999999999999999999999999933 times the speed of light according to Earth's reference frame). What's your speed if you moved 5 meters in however many years? Not even close to c. But again, you're at rest in your frame anyway (and feel an artificial gravitational field). (note: it will look like 5 meters once you hit that speed, but don't lose track of the fact that the faster you go, the more contracted things will get, which means the slower you were, the LESS contracted things were; this post is a vast oversimplification).

In other words, according to the space ship, you'd be able to reach anywhere in the universe without ever hitting the speed of light. This is the important part of all that. As for how long that will take, well that's another topic (according to convertalot.com that would take about 16.5 years accelerating at 1g. Which means there is significant length contraction along the way, but not to the point that 5000 light years becomes 5 meters. Since we're accelerating, that 16.5 years is NOT constant. As time goes on, you'd be able to cover more "Earth measured" distance in less time per meter, but as for you, you'll never move a c with respect to the world around you. It will just keep getting more and more contracted in your direction of motion).

If anyone wants detailed proof about why this would happen, I challenge you to take some time to learn about the reasons why special relativity and general relativity were needed in the first place. It will require a lot of work on your part. If you don't want to do the work, don't be an arrogant fool like that John guy who just called all of relativity "garbage" simply because he couldn't understand it. We could pretty easily see why length contraction and time dilation have to be true, because it only requires algebra and at most basic calculus, but when dealing with acceleration things get a lot more complex. Fortunately the clock hypothesis is experimentally true, which helps with that, but I'm rambling off topic now.

Point is, if you believe in observable reality (and verified experiments), we know that due to characteristics of space and time, no one will ever see anyone accelerate to the speed of light, so the question is like asking what's the color of middle C.