I am probably terribly wrong in my approach, but I treat DS's anxieties as if they were possible/realistic/etc and ask, well, what do we do about that? Car sickness - okay, let's pack some sick bags, and some anti-nausea gum and is there anything else you want? A change of clothes? Let's be prepared!
This is pretty much what I would have recommended. I think it's very useful to begin instructing a kid like this on risk management. Okay, here's a risk... how likely is this? What can we do to prepare? What can we do to respond?
For example, if the kid is worried about being carsick... has he ever been carsick before? That'll tell you how likely it is. Then you can start on your preparations, like what epoh says here. And then your response... what kind of signal should we have that you're about to be sick so we can pull over? After it happens, stop at a truck stop for a shower? Where are those along the way?
And then, of course, after it's over and nothing happened (assuming he's never been carsick before), say, "I told you so."
For the kid with the E-coli anxiety, I'd give them a blacklight, and explain how ultraviolet rays kill microbes like E-coli. Just shine the light on your food before you eat it, and you should be good to go. I'd also take the time to explain how the cooking process eliminates this as a problem. Then, a couple hours after eating the same food with no UV, I'd say, "Look, I'm fine. Told ya."
