Going through X-ray is sometimes a worry for the noise may frighten the cat when being taken out of its transport for inspection. Be prepared for the cat to scramble, hold tight, and reassure the animal. Also a pouch of litter in your carry-on may startle the inspector, so be prepared for questions. If travelling by car, have an adequate size carrier for your pet. If the cat appears to be nervous, try covering the carrier with a towel or sheet, but allowing for air flow.
Some cats prefer to look out while travelling and are quiet when they can see where they are going.
Most likely your cat will let you know, within a short period of travel, what they prefer. Having personally travelled thousands of miles with my cats by plane and by car throughout the years, there have never been any serious problems with the health and nature of the cats. I have never found the need to use tranquilizers to calm a cat. The motion, engine hum, and darkness of a carrier seem to keep the cats calm enough. There have been a few jangled and jogged nerves in part, but everyone survived to tell the stories of their amazing journeys.