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Truckers drive much longer distances every day, and the highways you are likely to take (particularly I-95) are major arteries of the US highway system. This is most likely safe, as long as you take reasonable precautions:
Upvote:0
To look at another angle of safety of the car and yourself, carjackings are incredibly rare on the interstate simply because of the speed of the vehicles involved (and not involved too). And then the entire state of New Jersey have only seen 184 carjacking offenses in 2016 according to the report and only 17 of the 565 municipalities reported even one. So, the chances of a bump-and-rob is nil on the long drive and not significant on the other end either.
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There's some level of risk in all travel. And risk in staying at home, for that matter. So there's no way to declare a certain trip to be objectively 'safe'. Best you can do is make sure your car is in good shape and that you know where you are going.
VA to NJ is a not a very long drive at all. So if your parents are concerned, why not drive there and back once w/ a family member first? You can probably even do it in one long day if you really want to, switching drivers as needed.
Upvote:2
There are quite a few variables, but yes, it should be safe. Get AAA if it helps you sleep at night.