This question is only concerned with the law in Victoria (Australia).
Let's say the traffic police spot a car, which is travelling at the speed limit, that they want to stop and question but the other car is on a different road or on the same road but travelling in the opposite direction.
The police have to slow down, or maybe even stop to make their turn. The police can't catch up to the other car without speeding, or waiting for the other car to slow down. Assuming the other car is on a highway, or otherwise unlikely to slow down soon, are the police allowed to speed without using lights or sirens until they catch up with the other car? This is particularly applicable to unmarked cars since most other drivers will be unaware that it's being driven by the police.
If they are allowed to speed, what's the maximum speed they can do without using their lights and sirens? Is there a maximum with lights and sirens? Do they have to radio for permission if they go above a certain limit?