While everyone’s answer of “gears” is close, I don’t think that’s the answer you are looking for. The motor in the car does not stay synchronized, as you describe it, with speed because of the torque converter.
The back of the motor has an output shaft. That output shaft is carrying all the “twisting” power the engine outputs. In a vehicle wtih an automatic transmission, it goes into a torque converter. It’s a donut shaped part has a fluid in it, and 2 “fans” facing each other. [Here](https://resize.hswstatic.com/w_285/gif/torque-cutaway.jpg) is a diagram.
The “fans” spin the fluid, so the fan on the input side spins the fan on the output side (which is the side that goes to the transmission to power the wheels).
The reason the car doesn’t spring forward is because of this fluid coupling in the torque converter. It’s also why when you stop, the transmission can stay in gear.
The torque converter has a “stall” speed. This is the fastest the engine can turn, in RPM, before the torque converter can no longer just absorb the engine and MUST turn the output shaft or risk damage. For example, my Yukon stall speed is around 1600RPM. That means if that if I press the brakes and the gas, at around 1600RPM the torque converter is done, and I better take my foot off the brakes because something is going to break.
Torque converters do have a “lockup” that makes them 1:1, where clutches essentially make the output shaft match the input shaft speed. It’s generally part of the higher gears (my Yukon, for example, locks out in 5th and 6th).
Automatic transmissions are amazing pieces of engineering, what a GREAT question!
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