My Lab did try to jump out of the car while it was moving, once. He was sitting in the back seat. I was in the front passenger seat, with my window down. He jumped over my shoulder, out the window. I grabbed his leash and pulled him back in. Let me tell you, a male Lab is not a light weight!
My cats didn't like to ride in the car. One time, one was loose in the car and got under my accelerator pedal! A very dangerous situation. From then on, no matter how much they fussed, they had to be in a kitty crate in the car.
When we had to be in a hurricane evacuation, we were in the car for almost 48 hours. I discovered that the cat stayed calm and in place if he rode in his covered litter box. Not ideal but if it made him happy under a temporary stressful situation, then it was OK.
Years ago, when we had a Pekinese dog, she rode on the front passenger seat of the car with Hubby driving, going to the vet. At a stop light, Hubby was rear ended by a careless driver. Little Ping went sliding off the seat and down into the area under the dashboard. I think the reason that she didn't hit the dash or windshield is because Hubby's car at that time was a Dodge Dart with a raised rear end. That means, the car sloped down and forward.
So, yes, dogs will go flying in an impact, even a minor one.
I have read news articles about traffic accidents where the dogs disappear from the scene. They get thrown out, and in fear, they just start running away. Sometimes they survive the accident but get hit by cars going by.
