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At first, he's not sure what's happened to him or how it had happened. Everything feels different in every single part of his senses.
Even his bones feel like they've somehow become stronger than they were before.
Eventually, his mental confusion clears up enough that he realizes what happened. One of the scientist's spiders at the science lab that his class had visited over the past week must have gotten loose and had gotten him.
Peter has no idea what to do with his new abilities until he hears about the Avengers and decides that he too can help people.