The acceleration pushes your back into the seat, and you brace yourself by pushing your foot harder against the floor (gas pedal). It's an instinct thing, not a physics one.
As a child I drove a lawnmower where the acceleration caused you to lean back, moving the levers back causing you to go in reverse, shoving you forward, causing you to drive forward, ...
It was actually the acceleration causing the back and forth (threw me off the seat before I let go causing it to stop).