I'd go with Staaf's idea. Create a track or two, set a countdown timer, and then have the player's move through the course within that time. For the brake part, have it as Staaf said, a spot where you have to stop between. So, the player will be going fast as they have to beat a certain time, but they also have to stop, so... yeah, you get the idea.

For an example of that concept in an actual game, check out Crazy Taxi.

If I were you, I'd make a drag racing game. It'd be really, really simple to implement in 2d, and the player could modify several different types of cars to race in. You could have advanced controls for acceleration, trying to balance the car between being a bloody fast drag racer and a full-on rocket. You could also have advanced braking controls, allowing the player to experiment with disc brakes and parachutes for slowing the car down.

You could add other modes into it incorporating the straight road idea. One thing you could do is have a road dotted with speed cameras and have the player gain time bonuses by passing checkpoints in as little time as possible without getting ticketed by the speed cameras (ie. by slowing down to below the speed the cameras will catch you at).

And the braking to a halt could be a sort of parking minigame, testing reflexes as you speed down a straight road and then have to brake when the parking space appears.

Hope that hepls you.