So simples it hardly calls for a solution but....
Obviously you will need to be in a pursuit, Give a copper a good ram up the arse to get their attention (or something to similar effect) then when the powpow is on your tail and you are not in a cool down period you simply go to a 'Jack Spot' which is where you change your cars over, These are located all around the map and are usually pretty easy to spot as they have a great massive manufactures badge hovering and rotating above them.
In reading this solution you are most likely doing so before you have played the game as you unlock this pretty much from just driving about messing around.
Easy peasy. Achievement Unlocked.