Using Calculus to Make Racing Games Involving Acceleration

by McKenna Harkin

Submitted : Spring 2022

            This project focuses on applying calculus to computer science, specifically using calculus to theorize how one could go about creating a graph to show the acceleration over time of a vehicle after you finish a race in a video game using calculus. To do this, I will investigate how calculus can be applied to physics. I will focus on how calculus is applied to the acceleration over time of cars, that could later be applied to creating a feature in a video game.

            The results are that acceleration is the derivative of velocity, and velocity is the derivative of position. Assuming the racing game can provide the position of the vehicle, we can then go about finding the velocity of the vehicle, and then finding the acceleration over time to display a graph on the screen for the player, so they can see their acceleration over time after they finish a race. This can also be done in reverse because the antiderivative of acceleration is velocity, and the antiderivative of velocity is position. Depending on what is needed, you can use derivatives and antiderivatives to find exactly what you need.

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