Because there’s already a very simple system for implementing reverse versus drive under the hood.
The gear settings on a car already change some number of engine rotations into some number of tire rotations. Gears are in place so we can adjust the ratio between engine rotations and tire rotations through different settings to keep the engine rotations within a certain range where it won’t stall or break.
One thing with gears is that every gear in a sequence changes the order of rotation. If you had a series of (2d) gears and turned the first one clockwise, the second would go counterclockwise, the 3rd would go clockwise again, the 4th counterclockwise, and so on. We can take advantage of this since we’re already using gears in the car.
If we add one extra physical gear into the sequence for reverse, the end result is that the tires turn the other way when we go into reverse.
Other than the gear issues it’s for safety.
Now as for the gears:
A car moving forward in gear cannot shift to reverse without causing mechanical issues (breaking very expensive parts). Most cars have an override that prevents the transmission from shifting to reverse unless the car has come to a stop (or very slow). This prevents damage to the gears and tires.
Now from a safety standpoint, let’s pretend that you replace the gears with a belt drive or an electric motor. Now you could have a reverse pedal, but there’s the risk of someone hitting reverse instead of the brake. So instead of stopping they’d end up going backwards.
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