How long would it take a normal spacecraft (not using solar sails or ion propulsion) to get to Alpha Centauri?
That's a great question! Regardless of what method you use to push the spacecraft, one of the major limitations is that people can't be accelerated by much more than the strength of gravity. However, if we were able to accelerate a space craft at the acceleration that we feel on the earth due to gravity, one would be able to get to half the speed of light in about 1 year. Since Alpha Centauri is about 4.4 light years away, at this speed it would take approximately 8 years to get there.
However, if we were sending a robotic spacecraft, then it could be accelerated much faster than one carrying humans. From our perspective on earth though, it would always take 4.4 years at the minimum for the space ship to get to Alpha Centauri and another 4.4 years minimum to return - so we wouldn't see the space ship until 8.8 years later or more. The space ship however would experience somewhat less time than us because of special relativity. Hope this answers your question!