The car should be accelerated smoothly for the same reasons they were for braking, while the car moves from a point to the exit point of a turn. The car will have settled with a certain load on each tire, through a turn. A sudden change in acceleration or a change in applying the accelerator of the car can disturb the available traction on one or more tires and take the car out of control. Using the accelerator in a controlled manner is a matter of depressing and releasing the accelerator in smooth actions. Sudden jerks in the pedal position are not recommended.
Applying the accelerator smoothly or accelerating smoothly in a typical street car is not as difficult to master as on smooth braking. Most street cars don’t have enough horsepower to cause trouble under most acceleration circumstances in case the car is moving fairly fast. Even the factory exotics and highly modified streetcars rarely have more than 400 horsepower, and in a car weighing 2500 to 3200 pounds, that just isn’t an overabundance of power to learn to control. A typical open wheel car can weigh between 1500 – 1800 lbs, and used to have 700-900 horsepower. This is about five times the power to weight ratio of a typical sports street car. Nevertheless, whether it is relatively easy to control or not, the introduction of 5 hp too much at the right point, you may as well have an extra 900 hp. While the car comes out of a turn and the car begins to straighten out, gradually increase the power as the car get straighter. Pedal pressure applied should be smooth and consistent. Dithery on and off stabs will slow down the car than a smooth increase.
Since most streetcars are not overly sensitive to rough throttle controls (I agree that there are definitely some exceptions), there are possibilities of developing bad habits with the accelerator quite easily. Even though you may not have to be ultra smooth in accelerating the car to maintain control, having the discipline to develop smooth control will help the driver to improvise his lap times and should you have the opportunity to drive a car with higher or better horsepower, you will have the skills to maintain the car pointed in the right direction.