You will not "fly" inside the vehicle unless it is accelerated (and even then you will simply be pushed to the back unless the vehicle acclerates very quickly and by a huge amount). This is actually the (Gallilean) principle of relativity: a state of rest is indistinguishable from a state of constant velocity motion by the observer who is moving/ stationary. There is no absolute motion.
In regards to your question, the vehicle would have to accelerate at about 9.807 m/s^2 for you to experience a "fake gravity" effect (directed opposite the motion of the car) equivalent to that experienced towards the center of the Earth. This is the principle of equivalence that was used by Einstein to formulate GR. But if the acceleration is 0, you will stay where you are inside the vehicle, as your body is also moving at the same velocity as the vehicle. You will "feel" that you are at rest. The only way you can "fly" inside is if the vehicle is undergoing acceleration (which is quite absolute), which your body will resist (inertia) and you will be pushed behind. As to where you went wrong, I have no idea where v came from in your equation. The force equals to the rate of change of momentum, that is $$F=\frac{dmv}{dt}=m\frac {dv}{dt}=ma$$ (I've used the classical assumption that mass stays constant for simplicity) As you can clearly see, the magnitude of the velocity in itself has no impact on the force.