It's common knowledge that one of the things that makes stealth aircraft so stealthy is that the body is covered in a skin of special material that interferes with radar. Would it be theoretically possible (for a more-or-less reality-based superhero concept) to create a "stealth car" based on the same principle, that won't register on a cop's radar gun?
The radar guns used for speed measurement are an extremely primitive form of radar called continuous-wave radar that just compares the frequency of a transmitted and a received signal to determine (based on Doppler's formula) what the target's speed is. Whereas the air radar you were referring to is a highly sophisticated pulse-based form of radar that uses advanced processing to reconstruct both distance, speed and azimuth/elevation information about the target. So the radar gun definitely would be trivial to jam through actively emitting a signal in its operating frequency. With the right materials, you could also build a car that has such a small radar cross-section that it simply doesn't pick up on the gun. Because the reflected power decreases with distance to the 4th power, this would be hard to do. However, you wouldn't need to make it perfectly invisible, but just so small in terms of radar cross-section that other vehicle or the ground have a stronger reflected signals.
Therefore, my conclusion: Yes, you can build such a car. My understanding is it would even be legal under FCC regulations, since you're not emitting anything to jam. However, the difficult choices in materials and the design sacrifices you would have to make in other areas (no sharply curved surfaces, shrouding of the exhaust, etc) would not make it worthwhile.
Let the arms race begin!
Let's start by saying yes, it is theoretically possible but no, it's not practically possible. Being stealthy in the air is very hard to do. Being stealthy on the ground against current radar/lidar speed guns is tricky at best.
If one designed a car to bounce radar and IR energy somewhere other than back towards the radar gun, then it would be difficult or impossible for the radar gun to get a good enough measurement. If this technique worked, the radar gun would think it is pointing at empty sky.
Passive measures will deal primarily with the shape of the car. Highly angular surfaces that reflect the radar away from the gun should be effective. Basically, you'll get a car that looks like the USAF F-117.
You'll need a specially shaped car, with radar/IR absorbent paint. Also, ensure that all of the bits on your car will contribute to sneakiness. Having a giant cooling fan hidden in your front grill could make you stand out like a lighthouse, even if the rest of the car is very sneaky. Side view mirrors could also ruin the sneakiness. You'll have to be very careful with the shape and reflectivity of all car parts....like the shape of your wheel rims (if radar goes through rubber).
The plus side to passive measures is that it's not illegal to make a weird shaped car. If you go with curved surfaces, no one will probably even notice. If you go angular surfaces (a la F-117), you'll have a very distinctive car....that may look something like this: ...except without two giant radar reflectors on the front in the form of wheel rims or the extra fiddly bits to form nice big radar reflectors. Remember that the corner reflector is one of the most efficient radar reflectors there is, so avoid that shape in your car if at all possible.
In short, yes, you can make a passively radar/lidar sneaky car, it's just crazy hard and very expensive.
In the Vietnam war, with the advent of surface-to-air missiles, an arms race began between radar operators and the aircraft flying against them. The aircraft would get a new jammer that would decrease the effectiveness of the radar, so the next generation radar would hone in on those jamming signals. Then the jammers would get a little bit more clever in how they jam to defeat the radar's new detection ability....you can see where this is going. The race continues to this day.
So, ignoring that active radar jamming is illegal, and laser jamming sometimes illegal, your active jamming measures must compete against the radar/lidar guns themselves. If lidar guns develop that can detect active jamming attempts, your jammer will need to account for that. If they send out lidar pulses in carefully coded bursts to ensure that the laser light coming back came to the gun came from that gun, you'll need to account for that too. Conceivably, radar/lidar guns could start to use quantum cryptography on the light they send out...let's hope it doesn't get to that point.
If this car is just avoiding speeding tickets, it's likely not worth it. Let's assume a perfect stealth car, invisible to lidar and radar. When you blow past a police officer, they will see you go past. Even if they don't know exactly how fast you were going, they will know that you were going faster than you should have which is enough for him to give chase. Stealth airplanes are designed to work beyond visual range where radar is the only way to detect an airplane. A stealth car inherently works within visual range so mitigating radar and lidar doesn't make as much sense.
How much is it worth to you?
What kind of threat are you attempting to counter with this car? You could easily spend many millions of dollars in passive and active countermeasures. If this is just to avoid getting a speeding ticket then your cost-benefit ratio is completely bonkers. If this is for a super-secret billion dollar delivery then sure, it's worth it.
In short attempting to do that would be rather impractical.
The stealth aircraft reduce their radar cross section primarily in two ways: shape that reflects the radar waves away from their origin and radar absorbent materials. Those measures aren't perfect but they reduce the target's visibility to radars, which makes it a lot harder to acquire and maintain lock on it, which is primarily useful for avoiding stationary SAM sites. However if the airplane passes too close or is poorly oriented it can still be locked on and shot down. Which is why it is not a very practical solution for a car, as the car will be radared from very close range where even minor imperfection can give sufficient return, and the cop radar doesn't need to maintain lock for 30 seconds to tell speed.
Conclusion: you'd be much better off jamming or spoofing it (which is actually not that difficult in real life), rather then bother with stealth.
Since you can be tracked by visual means (as mentioned in other answers), you really need to think about a different means of avoiding detection: metamaterials.
Metamaterials are engineered substances which can refract light or other energy in directions that the engineer desires, rather than the direction that happens naturally (much like a pencil in a glass of water):
Since refraction depends on the wavelength of the incoming energy, metamaterials designed to refract light will be different from metamaterials designed to refract radar. Metamaterials can be designed to cloak submarines from sonar, and even theoretically refract shockwaves from earthquakes around buildings (on that scale they would look like an irregularly spaced group of pilings driven into the ground around a building).
With proper design, metamaterials could refract light around an object in such a fashion that the observer isn't even aware of the object, there will be no "hole" in their line of sight.
The downside of metamaterials is that they are tightly tailored to the wavelength of the energy being refracted. A sonar cloaked submarine will still be visible to the naked eye and radar on the surface, unless there are several layers of metamaterials overlain on each other. How they would interact is an interesting question, and to my knowledge, no one has done research on this to date. As well, most metamaterials utilize a technique called an "optical lattice", so the tiny spacing in the lattice are vulnerable to damage or being filled with dirt. This means unless there is very careful maintenance and driving, the benefits of having a metamaterial coating will be negated quickly
The irony is in order to best preserve your metamaterial coating you should drive according to the rules of the road, avoid speeding or otherwise putting additional stressors on your car that could damage or degrade the coating.....
I remember reading an article about this in Car & Driver about 1990. They said the best production car for this was a dark blue Ford Probe with no front license plate and the headlights down. They sighted minimal vertical surfaces on the front and a dark color.
Now that was for laser detection because that was the new thing. And the car was not invisible, but the detection range was reduced to 400' instead of a standard 800', enough time to visibly notice the officer.
The project car of a Camaro website used radar absorbent material (RAM) to make it stealth. Metal fenders and hood were replaced with fiberglass units with RAM beneath it. Lots of details are covered: http://www.camarotech.com/rcs.html
It is all based on passive absorption of microwaves.