Photography

Moving further away and using a longer lens might improve results, although I don't know what focal length your using now. With a panning shot if the car is fairly close to you, the camera is rotating a bit so your getting perspective twist as well as panning.

A bit of motion blur at the rear is probably helping the effect too.

If you're post processing you can also add a bit more motion blur. Photoshop has excellent motion blurring that allows you to set the path and exact blur. I've used it on shots to help the motion blur effect.

I tried it out in this image, I even separated out the image so I could have less motion blur on some parts of the image. I think it came out all right on these parked cars.

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https://preview.redd.it/6rri0xbo3j1c1.jpeg?width=2043&format=pjpg&auto=webp&s=0e3f4b0f894995e13889efa467d1ffd633068f61

If you don't move, and especially if you're close, you will only be abled to get a small part sharp because the perspective of the car changes. If you want the whole car in focus, you gotta stay in the same position relative of the car aka you need to shoot from any other vessle, moving the same direction and speed as your subject. If that's not possible take a tele and get a good bit of distance between you and your subject. That might help

The way that the camera rotates with the car as you pan will mean that the front and rear of the car dont have the same movement as you take the shot. The closer you are the more noticable this will be.

If you take the shot as its at 90 degrees to you it will have minimal effect and you can get the sharpest pan but thats not always the best composition!

Keep practicing! I dont add anything in terms of motion blur in post, this one is 1/6th
https://www.robertborowikmedia.com/portfolio/G000079ZKvWEyTgU/I0000G1fxnynYAHY

See how the car is similar level of sharpness front to rear as the car is roughly 90 degrees to the camera.

If the shot was more of a three quarter angle of the car you would see that part that I pan with sharp and the rest increasingly blurry due to the different relative angle and speed of the car in the shot like this one.

https://www.robertborowikmedia.com/portfolio/G000079ZKvWEyTgU/I0000ON_y235x_08

Thats at 1/100th but you can still see how at that angle its not phyically possible to capture the car sharp front to rear, if you see an angle like that with everything sharp its done in post and not in camera.

If your equipment will let you in whatever light you are shooting, try a smaller aperture. F8 -f11.

Unless the subject is a perfectly flat plane and moving perpendicular to you, you're not going to get it all perfect. You have to focus on one point on the subject not the subject as a whole. For a car I say pick either the center of a one specific hub cap, or a side view mirror (at least to start with) and practice getting that sharp. If you go for something towards the center, it might make the front and back out just a little as opposed to picking the very front and making the back be more visibly blurred.

Be sure to follow through. Start panning before pressing the shutter and keep panning after the shot

Try to get the car when it's most perpendicular to you and not coming at you at an odd angle (again at least to start) as it will make it easier.

But again, don't try to pan to match the whole car, that's a recipe for disaster. Focus on one point on the car. And follow through. And practice a lot.