The correct answer is option D, the medulla oblongata.

The medulla oblongata is a part of the brainstem, located at the base of the brain, just above the spinal cord. It is responsible for regulating various vital functions, including swallowing, coughing, and vomiting.

Here is a detailed explanation of how the medulla oblongata controls these actions:

Swallowing:
- Swallowing is a complex process that involves the coordination of various muscles and nerves. It begins voluntarily but quickly becomes an involuntary reflex.
- The medulla oblongata contains the swallowing center, which receives signals from the sensory receptors in the mouth and throat.
- The swallowing center then sends out signals to coordinate the contraction of the muscles involved in swallowing, such as the tongue and the muscles in the throat (pharynx) and esophagus.
- This coordination ensures that food or liquid is moved safely from the mouth to the stomach.

Coughing:
- Coughing is a protective reflex that helps to clear the airways of irritants and foreign particles.
- When an irritant, such as dust or food, enters the airway, sensory receptors in the respiratory tract send signals to the medulla oblongata.
- The medulla oblongata then triggers a series of events, including the contraction of the diaphragm and the muscles in the chest, to generate a forceful exhalation.
- This forceful exhalation helps to expel the irritant and clear the airway.

Vomiting:
- Vomiting, also known as emesis, is a complex reflex that helps to expel harmful substances from the stomach.
- It is triggered by various stimuli, such as toxins, excessive alcohol consumption, or motion sickness.
- The medulla oblongata contains the vomiting center, which receives signals from different parts of the body, including the stomach, the inner ear, and the chemoreceptor trigger zone (CTZ) in the brain.
- When these signals reach the vomiting center, it coordinates a series of actions, including the closure of the glottis, contraction of the diaphragm and abdominal muscles, and relaxation of the lower esophageal sphincter.
- These actions result in the forceful expulsion of stomach contents through the mouth.

In summary, the medulla oblongata is responsible for regulating important functions such as swallowing, coughing, and vomiting. It receives signals from various sensory receptors and coordinates the appropriate muscle contractions to carry out these actions.