Ablatives are mainly used as objects of prepositions. Those prepositions USUALLY don't involve motion, but that's not 100%.
Genitives are always used to show possession.
Nearly all prepositions that take ablatives are stationary in meaning. Nearly all prepositions that take accusatives involve motion.
Hold on a bit, and I'll find some examples for you.
Translation Help:
Where do Ablatives and Genitives fit into a Latin sentence?
How do you tell if a prepositional phrase is with an Ablative or Accusative?
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1 answer