"D" stands for driving. Basically the driver will leave the car itself to pick the correct gear for any forward driving. There are a lot of criteria for the car's computer (ECU) to consider which gear is appropriate or best for the moment. Here are some of them:
1, Throttle position: basically, how deep the driver step onto the gas pedal. If it's deep, the ECU will trigger and downshift of gears to help acceleration. On the other hand, if it's a light throttle, the ECU will pick the highest possible gear without running the engine at too low an RPM in order to save gas usage
2, Slope grade: Most new cars nowadays will have "grade logic" in the transmission ECU. When going up hill, the ECU may not shift to higher gear just to keep the engine at the right power band, and do the same thing at down-grade slope also to avoid the car running too fast (pulled by gravity). The grade logic will also help the transmission by avoiding gear hunting (when you drive the old car, you can feel the transmission is switching gears back and forth on up hills)
3, Lateral G-force sensor: on some sports cars, there's a sensor detecting how the car is turning, and will not upshift in the middle of a curve even the engine is approaching red line to avoid lose of control/oversteer
4, Velocity: Simply speaking, how fast is the car traveling. You can not get the car to 100 km just by using the 1st gear :)
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When you said some drivers are starting at 2nd gear, are you talking about manual/stick shift or automatic? For manual, starting at 2nd and not 1st gear will have slower acceleration, hence help not losing tractrion in slippery condition. Other than that, I can only say that the driver is just lazy to start the car in 2nd because he can shift one fewer time. This may or may not hurt the car, depends on how the driver modulate the clutch.
For automatic transmission, it's point less to start the car in "2" instead of "D", unless he's parking on downhill slope and he doesn't want the car to get to 3rd gear.
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And just a correction to the previous poster. Not all automatic transmission equipped car start in first gear. Porsche's tiptronic, in normal mode, will start at 2nd gear; Mercedes's E and S class are the same, too. Basically, they will not go to 1st gear if the driver doesn't manually choose "1" or "L" gear. The reason for this is that automatic transmission already has a higher final drive ratio gear, and if you combine that with a short 1st gear, the car may give a "jerking" motion when starting which may break the traction (tire squeal), and even jerking when car switch from 1st to 2nd gear.