A govenor is generally installed on a car to limit the top speed the vehicle may attain. It might be a good thing for parents to do for teenagers!
If you mean by govenor, a mechanism to hold the car at a constant speed, then it is generally called cruise control. There is software that notes the speed the car is traveling and applies throttle to maintain that speed if there is an upgrade. In general, cruise control does not apply brakes but will close the throttle which slows the vehicle to some extent.
A flywheel is used to smooth the engine out so you do not feel the power pulses when a cylinder fires. A flywheel also makes a car easier to get started in motion with a standard transmission where the user must regulate the clutch, gas, and engine rpm. With the added inertia of a spinning flywheel, which is directly connected to the crankshaft, it reduces the chance of stalling the car when first starting off.
If you ever watch races, the cars tend to spin their wheels when they leave the pits. If they do not do that, there is a good chance the engine would stall due to lack of rotational inertia. Race cars generally have very small flywheels because small flywheels allow for greater acceleration and less of a gyroscopic effect when corning. Also with a small flywheel, a car can be stopped faster.