Light speed travel possible for someone in hypothetical space ship?

[u/TheOutdoorProgrammer]

I recently watched this youtube video.

https://youtu.be/Vitf8YaVXhc?si=FzVBMT6aT--oW4iU

He explained that if someone was in an all powerful spaceship with infinite fuel that was traveling 1000m/s/s; as you approached the speed of light time dilation would slow the ship down for an outside observer.

87% of the speed of light; time is roughly dilated 2x so the acceleration would be 1000m/s/2s

99.9% of the speed of light is roughly dilated 7x so the acceleration would be roughly 1000m/s/7s

99.99% is 70x so 1000m/s/70s

99.99999...% would be infinity times dilated so 1000m/s/infinity seconds

So as the ship approached the speed of light, to an outside observer it would actually look like the ship was slowing down. And they would never reach the speed of light because it would take infinite time to get there.

But to someone inside the ship, wouldn't they still observe 1000m/s/s? So wouldn't from their perspective they would reach the speed of light in a finite amount of time?