If you're spent, you are completely worn out or exhausted. Almost everyone feels completely spent after climbing a mountain or running a marathon.
When you're spent, you've used up your reserves of energy, and when a physical item is spent, it's outlived its usefulness. Spent fuel, for example, has been burned and can no longer power a machine, and a rocket might power a space shuttle until it's spent and falls away. The adjective spent comes from the verb spend, "to pay out," which has the Latin root expendere, "to pay down."
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