BigB79

In my state we usually arrest them, but it is also at our discretion, If we don't arrest them then we issue them a summons to go to court  and either have the vehicle towed or have a relative or friend pick up the vehicle.

Most places you arrest them, indeed, and seize the vehicle.

A handheld radar would be cool too. Thats right I had a handheld radar in LCPDFR but every time I checked speed it would be like shooting the gun and people would run. I personally prefer laser to radar because of its ability to be more accurate, hence I suggested laser rather than radar. I already have a Constant on radar with the Passive Radar mod which I like alot.

yeah, I have noticed this issue as well
I can see why you'd do this but I feel it makes it too easy. I wish there was a halfway thing, because the fast running option in the trainer is too fast, but normal just gets frustrating.

The speed limit signs are really just scenery, they don't mean anything to the AI.

There is a game function for this. I believe it is H on the keyboard, check your game controls if not. 

It will be the name that is within the game's files. For example, to spawn the LSPD cruiser, you'd insert "spawn police". For the sheriff cruiser, I believe it is "spawn sheriff". It will give you recommended/possible options as you are typing it, and all you need to do is press tab to select the option.

You're best getting a trainer, as these help with a lot of stuff like this, they also let you change your ped to ANY of the peds or animals in games, so you can get some pretty cool combinations of peds and change their textures and such.
https://www.gta5-mods.com/scripts/enhanced-native-trainer
This one is by far the best one, it lets you spawn vehicles and weapons just like all the others, but you can mod your vehicle on the spot, changing it's colour, window tints and all that kinda stuff.

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That comes with a plate reader and speed radar.