I have a question my son wants an answer to. When a rocket blasts out of the earths atmosphere does the speed of the rocket change after it reaches space. In what way?I
That depends upon whether or not its rocket engines are still firing. The rocket engines accelerate the craft. As it gets higher in the Earth's atmosphere there is less air and so less drag to slow it down. Therefore the same amount of push will change its speed more. Note that the Earth's atmosphere doesn't have a hard boundary, it just gets thinner until it is effectively no longer there.
Aside from air resistance, there is another force that acts on a spacecraft: gravity. This will pull it towards the Earth, but its effect gets weaker the further you are away. If you are heading straight up, then gravity will slow you down, unless your engines are pushing you enough to overcome this. Of course, if you start fast enough, you can keep going up even though you are slowing down. Eventually you would get far enough away that the Earth's gravity is no longer important, but you will still have to worry about the gravity of other bodies, most notably the Sun.
If you were to settle into an orbit about the Earth, then gravity just keeps you going in a circle. It doesn't slow you, just changes the direction you are moving. You can think of it as falling with style.
If we were now to consider being in deep space, far from anything, then a spacecraft would keep going in the same direction at the same speed without its engines firing. This is just Newton's First Law of Motion. There are no forces to slow it down, no friction like here on Earth. This is one of the things that science fiction authors often get wrong: if a ship's engines were to fail, it shouldn't shudder to a halt, but continue to coast along at the same speed.