The Crew

There is a faster solution to this. Once you engaged with a police car and have one wanted star, drive away but just try to stay out of the search circle as close as possible. Once the countdown of escaping reaches 2 or 3 slow down, so that you just escape, but the police is still very close and visible on your mini map. Turn around and ram it again.
That way you can use the same police vehicle over and over again for more wanted stars, plus you skip the waiting for the cops to show up. I could sometimes get up to 20/100 pursuits with this strategy.
hope it helps and good luck

For those of you struggling to find cops after the calling all units update:

I've noticed if you do crate runs under "offenses"on the map once you complete it ( win or lose) you can engage the cops that are near you.

Quickest method is to hit a crate and stop. Cops will arrest you. Hit continue then ram the cop that just arrested you. The crate run will not count for the escapes if you choose to continue it. Also if you win a part for your car and apply it there's a chance when the screen blacks and reloads that the cops will despawn.

Simple as it sounds all be it a bit time consuming. The fastest way to start a police chase is to wait until you notice you are under police watch, the police car will show in red on your mini map. Driving into the police car is the fastest way to begin the case then either accelerate as fast as you can or destroy the police car whilst you have only one star. Do this 100 time and the achievement is yours.

You can check your progress by pressing then to show the quick snap menu. use to scroll to awards, select freedrive then rookie.

I'm not sure if there is a faster way to do this or not but I did it this way and it took me like 30-40 sec each time:

- Fast travel to a crate of ur choice, preferably those that are located on cities and have a big straight road (like Chicago or Detroit)

- Hit the crate to start the mission and go to the menu straight away and abort it

- Hit the cops that spawned until the police chase starts and then go into the straight. U can use EMP if they are too close to u (if u dont have EMP equipped go to the menu , then "Abilities" and select "EMP Shock")

- Then just keep on going in the straight, most of the times it will be enough for the escape timer to run out because u only get 1 or 2 stars. However, on some straights it can spawn a road block (for example in Chicago), so just keep going and stop right before the road block detection zone and wait there. It should be enough for the timer to run out, on most scenarios.

- Repeat

Beware that sometimes there are cops that spawn without detection zone. They can still spot u, even though they wont chase u.

Being the buggy mess this game is, there are some bugs that sometimes can occur, like u getting 5 stars on u as soon as the chase starts or no cops showing up when u start the crate mission. If u get the latter, restarting the game fixed it for me.

Meanwhile, if u are also after the 10k award points achievement, there are some awards u can do while doing this:

- Complete 10 (and 25) police chases in a Street Spec vehicle (10 + 15 AP)

- Complete 10 (and 25) police chases in a Dirt Spec vehicle (10 + 15 AP)

- Complete 10 (and 25) police chases in a Perf Spec vehicle (10 + 15 AP)

- Complete 10 (and 25) police chases in a Raid Spec vehicle (10 + 15 AP)

- Complete 10 (and 25) police chases in a Circuit Spec vehicle (10 + 15 AP)

- Escape the police 15 times without using Nitro (5 AP)

- Escape the police chase while the arrest bar is over 65% full (10 AP)

- Maintain a police chases in Freedrive for a combined total of 100 km (20 AP)

- Lose the cops while maintaining a Stunts combo (15 AP)

These are the cars I used for this and their levels just so u know whats enough to do this (the only one I struggled with was the Raid one, but it only took a little bit more time, not much of a problem):

- Street - Volkswagen Golf GTI (794)

- Dirt - Nissan Skyline GT-R (684)

- Perf - Dodge Challenger SRT-8 (751)

- Raid - Dodge Challenger SRT-8 (749)

- Circuit - Ford GT (830)

Also, if u want u can check ur progress on this in Map > Driver ID > Awards > Freedrive > Rookie

Good Luck!

Giddex has a good idea for those that want to get it done faster definitely with the servers shutting in a few months. look for a crate in the city. Activate it sit and wait for the bust to happen. Then hit one of the cops before they go away. You then can use turning on different roads and Nos boost to get ride of them. Then it's nothing but rinse and repeat.
Keep in mind you can do this in a crew up to 4 so no one fighting over this and even f you're to help the escapee to escape it will still count to anyone helping out too. Just have to be close when it triggers or wait for it to pop on your screen.