Yes but to maximize that force, you want to maximize power. So if the driver is trying to accelerate as fast as possible, he'll keep the engine as close to peak power RPM as possible. He's basically trying to keep the power output constant.
For the sake of this topic, assume that he succeeded perfectly. How he does that is another topic.
Your gear ratio is constantly decreasing and so is your rotational force at the wheels.
^ That's the important bit, rotational force being torque.
That's the thing... as the gearing changes, the distance moved by the force over time changes.
It doesn't. The force of the engine turns a crank. The crank travels the same angular distance as long as the engine is operating at the same power (RPM). It is a steady state system. Power is constant, acceleration of the crank is constant, force on the crank is constant, the velocity of the crank is constant (assuming infinite changes to gearing), the torque from the engine is constant.
The only thing being changed is the gearing attached to that system. Incidentally, that's not necessary. Imagine an engine where the wheels were turned by electromagnetic force rather than gears.
What threw me off about this was the idea of Power =Mass Acceleration Velocity. (Derived from Power = Force Velocity) Because you'd expect that, classically, acceleration should remain constant with constant force.
An engine does exert a force, but not directly on the car. It exerts it on the wheels. To keep Force constant at the wheels as wheel speed increases, you have to increase acceleration at the engine, because:
F=MA or... F = M * D / T
The work done by the engine is the torque multiplied by the angular distance traveled (360 degrees). As velocity increases and you go to smaller and smaller gears, the angular distance traveled increases, but with smaller and smaller gears, the torque decreases (force on the gear is the same, radius of the gear decreases, fxr=torque, torque decreases). So the rotational force (torque) goes down, but the distance it is applied (rotational motion) goes up. The torque goes down linearly with the inverse of the radius of the gear. The angular speed goes up linearly with the inverse of the radius of the gear. The net result is no change in work.
The time that the wheels take to complete a rotation decreases at higher velocities, so force gets lower and lower the faster the car goes.
Torque gets lower and lower because the size of the gear gets smaller and smaller. The tangential force acting on the gear is the same, and the tangential force the gear imparts is the same.
