Calculating Run Time Analysis on Program Designed to Derive Kinematic Velocity and Acceleration Equa

by Christopher Humphrey

Submitted : Fall 2012

Run time analysis is a classification in the field of computer science used to evaluate the complexity of a program and the amount of resources (space and time) used to execute the program itself. A program can take anywhere from a few seconds to a few years to run, depending on the algorithms it uses as well as how long or difficult it is to process the information entered using the given algorithms. Given this information, it can be concluded that being able to analyze the run time data can help produce a program that is more efficient to run, and can be beneficial when marketing certain programs or algorithms to use in programs. Run time analysis is usually denoted in Big O Notation. Big O notation is used to describe the behavior of the algorithm or function as the argument or limit approaches a particular value or infinity, usually in terms of simpler functions. In computer science, Big O notation is generally used to show how algorithms respond to input size.

The program created was created using Python’s coding language to take an input of: P = 1/2AT^2 + VT + P and determine the linear velocity and acceleration of an object in motion. In physics, students are taught that the derivative of the above equation (position of an object in motion as opposed to time) is the velocity equation, and the derivative of the velocity equation is the acceleration of the object in motion. The program created automates this procedure, and can also be used to take the first and second derivative of any polynomial with powers greater than or equal to zero. The equations this program goes through (when using the basic projectile-position function) are: P = 1/2AT^2 + VT + P, V = AT + V, and A = A.

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