I'm doing a nice beef roast in the crock pot today. Normally I roast the carrots and potatoes together in the oven but due to other things I need the oven for I'm going to add them with the roast. I really want to avoid mushy vegetables but not sure how long before the roast is done that they should be added. I'm using "baby" carrots and diced potatoes about the size of a golf ball. I'm looking for cooked but firm. I have very little liquid in the bottom of the slow cooker as well.
Don't forget that opening the slow cooker to add stuff will add significant amounts of time to the overall length of cooking, especially in a fairly dry recipe.
If root veg isn't immersed in liquid it cooks extremely slowly in a slow cooker, so I'd be more worried about underdone than overdone in that case. You can cook jackets in there but I've never done it myself.
I would suggest adding them at the beginning; even then they may not be done if they're above the minimal amount of liquid you're using.
There's a trick that you can use to avoid mushy vegetables -- add acid.
Might as well just add the vinegar to the potatoes after they're cooked, right? But there's a very good reason to add a little vinegar to the potato's cooking water: it prevents it from overcooking, something I learned a while back when I was on my quest for French Fry perfection. Pectin breaks down much more slowly in acidic environments. A tablespoon of vinegar per quart of water was enough to allow me to boil my potatoes without having to worry about whether or not they'll overcook while I'm distracted by the dog.
ATK mentioned that too much vinegar would prevent the potatoes from softening at all. Unfortunately, I'm not aware of any resources that spell things out on specifically how the acidity affects cooking times.
I've recently tried a technique where I would add some vegetables at the beginning, removed the vegetables from the pot after a few hours and added a fresh batch of vegetables for the last 45min-1h. This allows you to get the flavors and better texture, but does introduce some waste.
Keep it simple while maintaining vitamins and nutrients. Microwave the vegetables until they are about 80% cooked...take a bite to test...they should have just a little crunch to them. Then add them for the last 30-45 minutes in the crock (cooking on high in this example).
Microwaving vegetables is the best way to cook them as it is the quickest. The quicker you can cook vegetables, the more nutrients they maintain. So having them in the crock the least amount of time is the idea here.
Most suggestions I've found say to cook the vegetables for 3 to 4 hours. Even in the official Crock-Pot manual they suggest that cooking vegetables takes longer than cooking the meat. Bad advice.
If you follow this advice you will be eating vegetables that don't contain most of their vitamins and nutrients and increase your chances of waste.
I agree with what most of the posters are saying. Especially "The quicker you can cook vegetables, the more nutrients they maintain". However my 1st concern is flavor profile so I kind of combine a lot of what people are saying into one method. 1) I typically sear the meat in cast Iron Pan to lock in the moisture and flavor. 2) I often make "yankee" style pot roast which often calls for diced tomatoes (Acid also helps break down the meat). 3) I grind herbs in mortar (Lightly) releases more flavor. 4) I add a moderate amount of diced veggies and a few small diced potatoes at the beginning (I want these veggies to break down so they add complexity to my liquid). 5) @ 1 Hr before the dish is complete I saute the veggies and add to the dish (I prefer this over microwave because microwave veggies tend to taste bland IMHO.) I saute them on higher temp until they are crunchy and underdone yet outside is slightly caramelized. It takes a little practice to get the veggies just right but when you do you will be rewarded with an awesome flavor profile that can not be duplicated in any other way. PS To the original Posters concern - If you cut the potatoes in half they saute well. in the above method.