Our goal is to find the time required for a 2009 Ford Mustang to accelerate from rest to 88 feet per second. We begin with three equations involving force, velocity, and force inverse, which is a value derived from Newton's Law, F=ma. The Mustang has three gears with three different gear ratios that must be used as the car accelerates. We found results from 2000 to 6000 RPMs for all three gears. Once the force inverse was found, we plotted the force inverse vs. velocity graph. The area beneath this curve from 0 to 88 feet per second is the time it takes to reach that speed. Using a Riemann sum approximation, we found that the time to be 4.109 seconds. This is a very brief time and is comparable to 5.2 seconds, the time found in a real test by RSPORTSCARS.com.
"2009 Ford Mustang Performance Test,"
Undergraduate Journal of Mathematical Modeling: One + Two:
2, Article 4.
DOI: http://dx.doi.org/10.5038/2326-3618.104.22.168 Available at: http://scholarcommons.usf.edu/ujmm/vol1/iss2/4
Arcadii Grinshpan, Mathematics and Statistics
Don Dekker, Mechanical Engineering