Your dog may be whining in the car because he's excited, nervous or sick. The way you deal with his whining will depend on what's making him whine. When you are working with your dog, always have a helper, either to drive the vehicle or do the training. Don't try to work with your dog while you are driving -- the results could be disastrous.
Dogs often whine while they are riding in the care because they are excited or anxious. Make sure you take your dog for a brisk walk or spend some time playing fetch with him first to work off some energy. Ideally, you want your dog to hop in the car and curl up for a nap. Taking some of the edge off his energy may be enough to put a stop to the whining.
Take Short Trips
Your dog may whine while he is in the car because he is doesn't have much experience riding in cars. To ease his mind, and teach him that going on car rides is no big deal, simply take lots of rides. Load him up, drive around the block, get back out. Don't take the same route all the time, but keep the trips short and pleasant.
Switch Things Up
If your dog only rides in the car when he is headed to the vet or groomer, it's really no surprise that he gets a little nervous when he's in the car. Take him for a ride to visit your parents, to a park where he can go for a walk, or just drive around with him. Your goal is to teach him that car rides don't always end in unpleasant or stressful locations.
Treat Motion Sickness
If your dog is uncomfortable riding in the car, he will probably whine. One reason many dogs experience discomfort in the car is because of motion sickness. Motion sickness is relatively common in puppies because of the immaturity of the ear canal. As your dog matures, he will hopefully outgrow motion sickness. If he doesn't, you can ask the veterinarian for medication to help, avoid feeding him right before car rides and try to keep him calm, as anxiety will worsen the symptoms.