Usages of поспать
Пусть он поспит на диване.
Let him sleep on the couch for a bit.
Ты болен, тебе нужно полежать и поспать.
You are sick, you need to lie down and sleep for a bit.
Я почитаю журнал, а потом посплю.
I will read a magazine for a bit, and then get some sleep.
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