It expresses both the distance of the point from the origin and its direction from the origin. The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. All observations in physics are incomplete without being described with respect to a reference frame. However, if the particle is constrained to move within a plane, a two-dimensional coordinate system is sufficient. In the most general case, a three-dimensional coordinate system is used to define the position of a particle. If the tower is 50 m high, and this height is measured along the z-axis, then the coordinate vector to the top of the tower is r = (0 m, −50 m, 50 m). For example, consider a tower 50 m south from your home, where the coordinate frame is centered at your home, such that east is in the direction of the x-axis and north is in the direction of the y-axis, then the coordinate vector to the base of the tower is r = (0 m, −50 m, 0 m). The position of a particle is defined as the coordinate vector from the origin of a coordinate frame to the particle. Particle kinematics is the study of the trajectory of particles. Notice the setup is not restricted to 2-d space, but a plane in any higher dimension. Kinematic vectors in plane polar coordinates. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and, working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. They are also central to dynamic analysis. Geometric transformations, also called rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of the equations of motion. In mechanical engineering, robotics, and biomechanics, kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. For further details, see analytical dynamics. The study of how forces act on bodies falls within kinetics, not kinematics. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. The goal of this first unit of The Physics Classroom has been to investigate the variety of means by which the motion of objects can be described.Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations ( position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s 2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s 2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop and you do not know the time required to skid to a stop.
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