Do I cover a pork roast?
The purpose of covering anything is to retain moisture as steam in the pan, instead of letting it evaporate away. So, using a pan that has a tight cover allows you to control the amount of moisture in the resulting cooked food.

Because you're cooking vegetables along with your pork roast, being able to cover the pan for at least part of the cooking time, can be helpful because it will allow the vegetables to steam, so they won't get dried out.

If you leave the cover on for the entire period, you'll steam the meat — it will cook, but it won't be as appealing. Start out with the oven preheated to a high temperature (at least 450F or so), and with just the roast in the pan, uncovered, just until the outside begins to brown. For a small or medium roast, this should be no more than about 15 to 25 minutes, and you may wish to turn the roast once or twice during this period.

Now add your vegetables, cover the pan, and turn the oven down to a slow temperature (285-315F). In addition to your potatoes and carrots, you may wish to add some chopped onion, celery, and/or green pepper. Those vegetables will release lots of moisture (especially if you add salt), and along with the meat, create a nice broth so your other vegetables won't dry out.

Cooked slowly along with the vegetables, the roast will be very tender and flavorful. It may take an hour or more, depending of course, on the size and shape of the roast. A meat thermometer is the best way to determine when the roast is cooked. For pork, the coolest temperature in the center should be 170F (77C), but take it out a couple degrees lower because it will still cook a bit after coming out of the oven.