When Vegeta is training in the space ship. He completely wrecks the place. After that he passes out because of his wounds. When Vegeta wakes up, he continues training in that same space ship (now in perfect shape again). There is no way that space ship could have been repaired that quickly.
You actually think they have only one of those spaceships? The one he continued training in wasn't the same ship as the one he started training in, which was destroyed.
What you should think of was that it only took Dr. Green a few weeks to build a spaceship for Gokuh out of the one he came to Earth in. But wait! The one he came in was destroyed by Piccolo when Gohan went oozaru. If it only took him a few weeks to do THAT, then it wouldn't take him that long to build another one. And besides, after an explosion like that, wouldn't you have been unconscious for a few weeks? Think about that.
Let me point a few things out, there were 2 capsules that Vegeta used. He blew up the 1st one and Dr. Briefs (There is no one on DBZ named Dr. Green) builds him a 2nd one and so what if it has the same number on the side of it.
Yes Dr. Briefs rebuilt the capsule spaceship. The numbers are for the type of capsules it is. e.g. capsule 1 is a dome house and there are hundreds of capsule 1s out there.
If you actually watched closely you would know it was a different one, Capsle 1 was used by Buruma Gohan and Kuririn, Capsle 2 was used by gokuu, Capsle 1 was used by Vejita and destroyed, and Capsle 3 was used again by Vejita, but was then stolen by Vejita.