Japanese adjectives (形容詞) form independent predicates, that means, they grammatically act as verbs (速い means "be fast"). Again, all verbs except for ones referring to "staying" (e.g. ある, いる, 住む, 泊まる etc.) mark their locations by
で. The same thing applies to all word classes (with the help of copula
Verb: 日本で走る run in Japan
Adjective: 日本で安い be inexpensive in Japan
Adjective noun: 日本で有名だ be famous in Japan
Noun: 日本で英雄だ be a hero in Japan
As an aside, your
doesn't sound natural as a complete sentence, unless you're reporting what happens in front of your eyes (journalists favor it for articles, though). If you simply want to say that "cars are fast in Japan", you'd topicalize one element:
日本では車が速い。 Cars run fast in Japan (neutral / compared to other countries).
日本で車は速い。 Cars run fast in Japan (compared to other transportations).