Final answer:
The preferred route for administering medication in acute care settings, such as after a severe MVA, is intravenous due to its fast onset and efficient drug delivery.
Step-by-step explanation:
In the most acute care situations, especially following a motor vehicle accident (MVA) with severe back pain, the preferred route of administration of medication is intravenous. This method is chosen because intravenous administration ensures rapid delivery of the drug into the bloodstream, leading to quick onset of action, which is crucial in an emergency scenario. IV access allows for immediate adjustment of dosage and can manage acute pain effectively. Other methods like epidural, subcutaneous, and intramuscular could be considered in different contexts, but for emergency care, particularly in the ER and for critical conditions, intravenous is the most suitable because it allows for fast and efficient treatment.