If you put your cat in a car and it throws up, your cat could be getting motion sickness. Just as people can gradually get used to being on anything that moves, so can cats. If you have the patience and the time, give your cat more frequent car trips, which your cat will appreciate if the car trip winds up at a local fish market, sushi restaurant, or pet store stocked with catnip.
Also if you know you’ll be driving your cat around, try not to feed the cat for four hours prior to your departure. Cats can’t throw up if they don’t have food in their stomach, but they can still dry heave like a teenager after downing his first six-pack of beer.
As a last resort, consider motion sickness medicine for your car. Generally getting a cat to take any kind of medicine will be more traumatic for the owner than for the cat getting motion sickness. If all else fails, consider just carrying your cat where it needs to go and skip driving altogether.