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The purpose of this project is to compare the first gear performance of an automobile for both its manual and automatic transmission options. Each transmission type has a different gear ratio, which yields a different acceleration curve for each transmission throughout the torque-rpm curve of the engine. The method of integral calculus was used to find an equation which could be used to solve for time at any point in the car's acceleration. The automobile velocity versus time was then graphed to compare each transmissions acceleration trend. This process is similar to that which automotive companies may use when determining what type of transmission to pair with a particular vehicle. By observing the trends in the acceleration graphs, it was determined that there are specific advantages and disadvantages to each type of transmission. Which transmission is the “better” choice is dependent on what application the automobile will be used for (e.g. racing, day-to-day driving, towing/hauling).

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

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Mathematics Commons




Arcadii Grinshpan, Mathematics and Statistics

Scott Campbell, Chemical & Biomedical Engineering

Problem Suggested By:

Scott Campbell