What is the value of a 2002 US quarter with an Indiana 1816 car on it?

25 cents. It's one of the state quarters issued from 1999 to 2009; hundreds of millions were minted.

And 1816 is the date that Indiana was admitted to the Union, not the date of the car. It's a modern race car from the Indianapolis 500. After all, there weren't any automobiles back in 1816!