On super speedways, they can reach speeds of 200 miles per hour. They are slower on short tracks.
Today, the fastest they can go is 202 mph.
Currently with the restrictor plate carbs, they can go about 190, at tracks like Talladega and Daytona. Which they are tracks where you run wide open all the way around and is too fast for safety. Other tracks such as California (Auto Club Speedway) and Atlanta Motor Speedway they run about 200-205 mph.
A Nascar car can usually get up to about 200 miles per hour on a large track. However though, there is a thing called a restrictor plate that makes a Nascar car slow down. They use restrictor plates strictly as a safety matter so the car does not get thrown into the air because of all the air. So I guess it really depends on what kind of car, what kind of track and what the rules are on the race track.
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NASCAR Cup stock cars are not built for acceleration from a dead stop. However, they are still pretty quick. In 2009, a Michael Waltrip Cup car was tested for 1/4 mile accerlation. They were able to run a 10.4@147, with the toughest part being the start. Current stats for a 2010 Cup car are roughly 860+ rear wheel horsepower (last official stat came in 2008 at Michigan where Kurt Busch's car made 839 rear wheel horsepower on a dynojet), and ~3500 lbs.
IT DEPENDS ON THE TRACK. THE FASTEST THEY GO IS ON RESTRICTOR PLATE RACES AND THEY CAN REACH SPEEDS OF 190 TO 200MPH