As cars work due to friction, I'm going to assume that you mean a system without any drag rather than no friction. So that 100% of the power of the engine is developed into increasing the KE of the car.
For this scenario, let's assume that the 200 hp engine is working at full power and producing 2000 N at the wheels.
Unfortunately, we can't do that with a real engine. For any real engine, the ability to develop force/torque decreases as the speed gets higher. In fact, you can use the speed and the power to find the max force at that speed.
At high speed the engine will still be able to accelerate the vehicle, but with ever decreasing amounts of force/torque.
But my question here is about the physical quantities rather than the true capability of an ICE. In other words and to make things simpler, let's use a 200 hp rocket producing 2000 N
This isn't a limitation of an internal combustion engine (or any engine). It's a limitation of how the force is produced. You only have two choices for producing the force:
- You're pushing against some external mass (like the earth)
- You're pushing against some mass you have with you (you're a rocket)
My answer above is limited to the first case. As your speed increases relative to the reaction mass, your ability to produce torque decreases. This doesn't matter if it's an ICE, an electric motor, a spring, or anything.
If you bring the reaction mass with you, then you are producing constant force, not constant power. But at the beginning, your system is horribly inefficient from an energy point of view. Whereas in the first case all of the energy of the engine can go into the KE of the car, in case of the rocket most of the energy is going into the KE of the exhaust.
At high speeds (when the rocket is going at speeds approaching the exhaust velocity), additional power comes from the fact that the KE of the now-accelerated fuel is reduced as it leaves the rocket.
A rocket can produce constant thrust, but not constant power. The power will change as it accelerates.
Here's one last way to think about it: The transmission from your power unit (engine) to your reaction mass (the ground) can be considered to be a moveable lever.
You have a choice with a lever, you can shorten the lever so that it produces high speed but reduces the force you apply, or you can lengthen the lever so that it produces lower speed, but increases the force you apply.
As your speed relative to the reaction mass increases, you have to bias your lever more to the "speed" side, which will reduce your applied force. In a car this happens through the gears in the transmission, but is true regardless of the method applied.