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This is one of those funny questions that pops up in lots of people's minds. As you're driving your car, you can imagine that it would be very easy to move the shifter into the "R" position at any time. You probably would never even consider giving in to your curiosity, though. Because you know that if you DID try it, it would cause the transmission to explode, or something like that. So, instead, you end up constantly wondering…
The reverse gear on any car with a manual transmission is an incredibly simple piece of machinery. There is a shaft that gets its power from the engine, and it has teeth on it that are used for reverse. There's another shaft that will drive the wheels, and it, too, has teeth on it that are used for reverse. To engage reverse, a gear literally gets pushed in between the two shafts to engage the two sets of teeth. It simply slides its teeth into the teeth on the two shafts and engages them.
So it turns out that the answer to this question is pretty anticlimatic. If you were to actually try engaging reverse while rolling down the road, the gear that has to slide into place is going to be trying to engage two spinning gears, and one of those gears is rotating rapidly in the wrong direction. What you will hear (and feel in the shift) is a very obnoxious buzzing sound as the teeth gnash against one another. However, there's no way to get the gear into place while in motion like this, so nothing will happen. The transmission won't explode. Nor will the car stop on a dime and reverse into oncoming traffic, even though that's what happens in cartoons.
About the only time you can actually get a car into reverse is when it's at a dead stop.