Now lets talk about why it takes so long to go anywhere in space. The answer is you usually have to take the long way around. In most orbital systems, all the objects tend to orbit in the same direction around the largest gravitational body. So all the planets move counterclockwise around the Sun. The Moon move counterclockwise around the Earth. And all the asteroids, including Ceres, in the asteroid belt also move counterclockwise around the Sun. So any spacecraft also usually moves counterclockwise around planets and the Sun.
In space, everything is moving in an orbit, always. Nothing stands still. And orbital motion generally requires no energy. The spacecraft, moon, or planet will continuously orbit without requiring energy to keep it moving. That’s sometimes a difficult concept to grasp. On Earth we know it takes energy to move. If you’re running around a track, you have to expend energy to keep running and it takes more effort to speed up than to slow down. That’s due to the effects friction and air resistance as you run. If we took away friction and air resistance, once you get up to speed, you’d keep going around the track without having to move your legs. In space there’s minimal amount of air (it is a vacuum after all), so without anything to slow objects down, things keep moving.
This fact tends to make rendezvousing with other objects difficult. Here on Earth, our everyday experience says that we can walk from our front door to our mailbox in a straight line because those two objects are standing still. However lets take the example of running around a track and trying to get to someone who’s on the other side of the track. You have two options, slow down and let them catch up to you, or speed up and catch up to them. On regular Earth with air resistance and having to expend energy to keep moving, slowing down would be the easiest and you’d expend less energy to do so. However on airless Earth or in space, since you’re moving for “free” you have to expend energy to slow down as well as speed up.
Now that we understand energy, in the form of thrust from a rocket engine, is needed to speed up or slow down, lets consider Dawn’s situation. Dawn starts at Earth, which is about 150 million kilometers from the Sun. For numerical simplicity, this distance is referred to as 1 astronomical unit (AU). So Earth is 1 AU from the Sun, and Ceres is 2.77 AU. To get to Ceres, Dawn first has to reach 2.77 AU, which means speeding up. Not only does it need to speed up, it has to time it correctly that when it reaches Ceres’s orbit, the asteroid will actually be there. It’s like hitting a bullet with another bullet, not easy. Plus 2.77 AU is a very very long way to travel, even at 10+ km/s.