“I got a flat.”
You were late for work this morning because you had trouble with one of the tires on your car. You're explaining to your boss why you're late.
I got a flat.
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When you're talking about cars and driving, a "flat" means a flat tire: a tire that the air has come out of.
You can either say that someone "got a flat tire":
I was on time, but then I had to stop because I got a flat tire.
...or you can just say that they "got a flat":
Would you know how to change the tire if you got a flat?