Gas engines only really work well in a certain RPM range, too low and the engine makes too little power, too high and you risk damaging it and use a lot of fuel.
Gears work by sort of trading speed for acceleration, so in first gear you trade off a lot of speed, to get a lot of force in order to start, which is why the engine revs up very high even at low speeds, but you accelerate really fast. Second gear you keep more speed, and so less acceleration. And finally in 5th or/ 6th you actually trade away acceleration in order to get more speed, and higher fuel efficiency.
This in short means the speed of the car is limited by how the speed of the engine and much speed the gear “trades away” so you have a speed range for every gear
This is absolutely the same in an automatic and a stick shift, just switching e tween these gears works is achieved in very different ways
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