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2D Motion

Kinematics Terms

Introduction to Motion in Two and Three Dimensions

Position, Velocity, and Acceleration as Vectors

Terms

Kinematics  -  Kinematics is concerned with describing the way in which objects move.
Displacement  -  An object's total change in position. If a man runs around an oval 400 meter track, stopping at the precise location he began, though he ran a distance of 400 meters, his total displacement was 0.
Dynamics  -  Dynamics focuses on understanding why objects move the way they do.
Reference frame  -  The coordinate system with respect to which motion is being described.
Speed  -  A measure of how fast an object is moving.
Average velocity  -  The time-average of the velocity function over a specified time-interval. (See formula below.)
Instantaneous velocity  -  The value of the velocity function at a particular instant in time. (See formula below.)
Gravitational acceleration  -  The graviational acceleration of objects near the earth's surface is the same for all objects regardless of mass and is given by the number g = 9.8m/s2 .
Scalar-valued function  -  A function that outputs scalars (regular numbers). Most common functions that you are probably familiar with are scalar-valued functions.
Vector-valued function  -  A function that outputs vectors. This means that while the domain of the function may consist of scalars, the values in the range are all vectors.
Position function  -  A position function can be either scalar-valued (for motion in one dimension) or vector-valued (for motion in two or three dimensions). At each point in time its value represents the position of an object at that time.
Velocity function  -  This function is the time-derivative of the position function, and gives the velocity of an object at each point in time.
Acceleration function  -  This function is the time-derivative of the velocity function, and the second time-derivative of the position function. It gives the value of the acceleration of an object at each point in time.
Time-derivative  -  The time-derivative of a function is a new function whose value at each point represents the rate of change of the original function with respect to time.
Simple harmonic motion  -  Periodic motion that can be described by special types of position functions. Examples of simple harmonic motion include an object moving in a circle and a ball bouncing up and down on a spring.

Formulae

 
The average velocity for an object with position function x(t) over the time interval (t 0, t 1) . v avg =
 
The instantaneous velocity at time t for an object with position function x(t) . v(t) =

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