Elapsed Time of Vehicle Acceleration

• Main Author: Jensen McTighe
• Format: Article
• Language: English
• Published: University of South Florida 2018-09-01
• Series: Undergraduate Journal of Mathematical Modeling: One + Two
• Online Access: https://scholarcommons.usf.edu/ujmm/vol9/iss1/5/

Newton’s Second Law states that force is equal to the mass of an object multiplied by its acceleration. More specifically, force is the mass times the instantaneous change in velocity over time of an object. By rearranging this equation, it can be determined that the time elapsed of the acceleration of an object is equal to the integral of the inverse value of the force relative to change in velocity (dv). In the context of real world application, this method can be used to calculate the time taken for a vehicle to accelerate from its minimum to maximum speed, given the values of torque output relative to engine rpms, transmission specifications, vehicle weight, and tire size. To demonstrate the viability of this method, the elapsed time of acceleration is calculated for a 2017 Ford GT with a torque-rpm curve containing 58 values. It is found that the resulting values are realistic when neglecting forces of friction and air resistance. The results obtained would be analogous to the values obtained through experimentation on a dynamometer, which allows the vehicle to be tested while stationary.