Your velocity is a constant number which is the issue.
For videogame purposes you can ignore all other constants other than velocity and end up with this, a simple model where a plane accelerates until it reaches terminal velocity.
This basically makes the assumption that your plane is a flying sphere with constant area, and assumes the air density is constant. You can ignore @Imperiector realism for this.
Ultimately all it does is it will prevent a plane from infinitely accelerating and allow the plane to deaccelerate.
To make a simple plane model from the above I would add angular velocity to turn the plane with roll that is inversely proportional to speed. (More speed harder to turn)
And an anti gravity forces that scales to body weight to simulate lift once it reaches a certain speed.