Kinematic Equations and Free FallHillal Faizy Plainview Old Bethpage John F. Kennedy High School Grade 11 11/27/17Background/Introduction “Kinematics is defined as a branch of physics that deals with aspects of motion without taking into consideration the mass of these objects. The goal of Kinematics is to provide a description of the spatial system of bodies or systems in regards to their velocity, rate at which particles are moving, and acceleration, rate at which the velocity is changing. Kinematics aims to provide a description of the spatial position of bodies or systems of material particles, the rate at which the particles are moving (velocity), and the rate at which their velocity is changing (acceleration). This is of interest due to its vast applications in real life situations. Kinematics can be experimented and observed by anyone with minimal lab equipment. One person by themselves did not invent or find Kinematics by themselves, rather many established scientists such as Henry Cavendish and Sir Isaac Newton have contributed to this branch of physics. Kinematics revolves around gravity, and Sir Isaac Newton had discovered gravity one day when an apple fell on his head. He also noticed that all objects fall at constant accelerations when neglecting air resistance. Henry Cavendish used this observation and went into depth by finding the rate at which objects uniformly fall, which is 9.81m/s2. The main kinematic equations are used to find a variety of different information when given a certain amount of given data such as distance or displacement, initial velocity, final velocity, acceleration, and time. The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object’s motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object’s motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object’s motion.The Kinematic Equations:d=vit + ½at2vf2=vi2 + 2advf=vi+atd=½ (vi+vf)tKey:d= distance or displacementvi= initial velocityvf= final velocitya= acceleration (usually 9.81m/s2 in the case of free fall)d= distancet=timeFor these kinematic equations, many different types of information can be calculated as shown above, when given certain information such as distance, initial velocity, final velocity, acceleration, distance, or time. All these equations are derived from integral and derivative calculus, as shown to the right, but is not the focus of this paper, but rather on the kinematic equations themselves. The principle of of Kinematic equations lead to each other in the displacement or distance, velocity, and acceleration. Instead of focusing on how to derive these equations I will be exploring the math of the equations when used in real life situations. An example of a kinematic equation can be as shown below:Peter runs 36 meters down a hallway at a velocity of 3m/s from rest. How much time did it take for the person to go from rest to end up hitting into the wall? First Write down your givens:Vi = 0m/sVf = 3m/3D = 36mT = ?Then pick which equation is the most fit and in this case it is as shown below:d=½ (vi+vf)tYou then plug in and solve mathematically36m = ½ (0m/s = 3m/s) t36m = ½ (3m/s) t36m = (1.5m/s) t t = 24sUltimately, Peter took 24s to run 36 meters, which can truly show how we are performing and engaging in kinematic equations in many different scenarios throughout our lives.So on Earth, we are sure that universal gravitation is -9.81m/s2, but, what if we when we make it to other planets, what will universal gravitation be there. Ultimately, I would like to find the universal gravitational forces throughout the universe so we could possible live and roam these planets one day with ease. It would be magnificent to have such a universe where we could go from one planet to another because of these kinematic equations and free fall.Free fall would be utilized as since we would want to find the universal gravitation we would need to see at what rate and accelerations objects fall, so we can make technologies to mimic these types of situations or essentially increase or decrease our gravitational forces, for the desired effect.Kinematic Equations can come into play when we would need to find how we would move about the planets. In Earth, there are minimal outside forces stopping us such as friction and air resistance but on other planets maybe there could be other outside forces which can impact us and ultimately the way people and objects are in regard to motion.Ultimately, we need to think to the future, and with the population rising quickly on Earth, we need to not only find new ways to get to other planets. But, we also need to think about other ways to live there successfully, creating the best and most comfortable lives possible. Moving to other planets isn’t such a stretch when you look at the numbers and the population growths. Ultimately, Kinematic Equations and Free Fall will be necessary to put in use when thinking about moving to other planets.”

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