pospieszyć (Polish) comes from Polish spieszyć, from Proto-Slavic spěšiti, from Proto-Slavic spěxъ, from Proto-Slavic spěti, from Proto-Balto-Slavic spḗˀtei, from Proto-Indo-European spéh₁-, from Proto-Indo-European speh₁- — to succeed, to prosper.
pospieszyć (Polish): to hurry