Position, Velocity & Acceleration: Transitional Motion In Applied Calculus

by Nicholas Keenan

 

Submitted : Spring 2022

This paper demonstrates the use of calculus applied in a real world scenario having to do with physics. In this paper, we will use calculus to show the relationship between position, velocity, and acceleration in terms of transitional motion. Differential equations can be used to show the relationship of these concepts with the derivative of an object’s position being the value of the object’s velocity and the derivative of the object’s velocity being the object’s acceleration. In the same regard, the relationship goes the opposite way as well with an object’s velocity being the integration of the object’s acceleration, and the object’s position being the integration of the object’s velocity. In this paper, we will solve for time in a function, and use that time to calculate the speed of an object.

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