Final answer:
Local anesthetics are classified as nerve blocking agents because they can temporarily block nerve conduction, causing sensory and motor paralysis in the innervated area when applied locally.
Step-by-step explanation:
The category of analgesic medications classified as nerve blocking agents is local anesthetics. These drugs work by blocking nerve conduction when applied locally to the nerve tissue in the appropriate concentrations. Unlike NSAIDs (Nonsteroidal anti-inflammatory drugs) which primarily reduce inflammation and pain, or opioids which bind to opioid receptors to relieve pain, local anesthetics prevent both the initiation and transmission of sensory impulses by acting on any part of the nervous system and on every type of nerve fiber. Hence, they can cause sensory and motor paralysis in the innervated area temporarily.