Almost every course has side paths (visible on the map) that can be shorter or longer routes as a racer or let a racer escape if you don't keep up as a cop...so you need to actually get familiar with the tracks.
You get more cars as you finish missions in three or four different 'classes' and usually only one class can be used on a particular mission, sometimes you need to use a particular car...usually one you wouldn't be able to unlock yet.
As a cop you basically run racers off the road by smashing them at high speed or use police traps...dropping spikes (I usually turbo dead in front a few inches and drop those lol), EMP blasts, roadblocks (which you can hit too), or call in a helicopter to fly ahead of them and drop spikes for you...which in my experience tends to backfire and take you out more often than them unless you dodge your own copter like a racer
As a racer you race and usually get chased as well, so you can use the other racers as police cannon fodder fucking them both up or just take out whoever you need to, cops will attack the Ai as well though. As a racer you get the spikes, EMP, a super turbo boost, and a jammer which can prevent the other weapons and police from calling in support.
It took me a really long time to finish all of the tracks with the gold medal (first place or minimal time), but you can open new missions by getting bronze (third place or required time), you can progress without ever really being stuck on a single mission since usually any mission opens new missions if you need a better car or just have an issue with the track...one of the best features in that game IMO--nobody wants to spend 2 hours trying a single race over and over again for a week lol.