Theory
Kinematics deals with the motion of objects. More fundamentally, it describes paths through space that objects can travel along. The shape of these paths are constrained by a set of differential equations that define velocity and acceleration. Velocity is a property of an object that describes the speed and direction of the object. Velocity is a vector. Acceleration is something that affects an object. It is an action that changes the velocity of the object. Acceleration is also a vector.
We begin with an arbitrary path. To describe the path we employ the common practice of constructing a coordinate system. In this way we can describe each point on the path in terms of coordinates and then genralize by describing the path itself as functions.
Assumptions
The one assumption of kinematics is that we can map a continuous coordinate system onto physical space. Additionally, classical kinematics also assumes a flat space (as opposed to relativistic kinematics). The most common coordinate systems for flat space are the Cartesian coordinate system, the cylindrical coordinate system and the spherical coordinate system. All of these are merely different schemes for describing the same thing.
The variables that define the function are the parameters. Any number of variables can be parameters to the coordinate functions. The simplest functions deal with only one parameter t, which refers to time.
| Examples |
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| Note: Since time is the only variable in the functions, everything else represent constants. |
The parameter of time can be represented on our path by incremental ticks, which in turn implies that time is a coordinate exclusive to the path itself. This is defined as the proper time of the object.
Note that t=0 is the moment we start our timer. Negative time is the time before that event. (Also note that in relativistic
kinematics proper time is denoted by
τ. The time, t, of an arbitrary observer is a coordinate variable in a four-dimensional coordinate system that maps spacetime.)