# Velocity

Speed (symbol: v, from Latin Velocitas ), also web speed is a key concept in classical mechanics. It is a vectorial quantity, characterized by the direction of movement and the amount. The sum specifies the distance traveled by a point of a body within a certain period of time. Figures refer to the amount of the vector quantity, it is shown for example on the speedometer of a car. The unit used internationally for speed is meters per second (m / s), are also in use kilometers per hour (km / h) and - especially in the maritime and aviation - knots (kn).

The highest possible speed for movement and information transfer is the speed of light.

More generally, the term velocity change of a physical size over time ( see rate of change).

## Etymology

Geschwind (adjective speed ) ' fast', Middle High German geswinde ' quick, hasty, impetuous, bold ', Middle Low German geswint, geswine ' strong' ( increased importance by the prefix ge - ), Middle High German swinde, swint ' powerful, strong, fierce, articulate, fast, nasty, dangerous '. Old High German presence is shown by names like Amalswind, Swindbert, Swinda.

## Definition

Along a curved path from the starting point A to the target point P distance covered is labeled S. In addition, the elapsed time t is considered to reach the point P. The ratio of the two gives the average speed.

DELTA.S for a section between the points P1 and P2, the time required DELTA.t. From this, the average speed results in the investigated road section.

Through the observation period? T reduced to a vanishingly small time interval results in a limit to the mathematics known as differential quotient or derivative of distance with respect to time. As a result, the instantaneous velocity.

A movement in the room has a course which is known as a web cam, and their description will be given by the position vector as a function of time. Since each change in position having a direction which is also the speed which characterizes this change in relation to time, represents a vector quantity

## Acceleration and jerk

The derivative of the velocity with respect to time the acceleration is:

The second derivative of the velocity with respect to time is the residue of a movement:

## Units

SI unit of speed is meters per second (m / s). Another common unit of speed is kilometers per hour (km / h).

In everyday language the term " miles per hour " used. As in physics, such a composition of two units (here: " Hour" and " km " ) is understood as a multiplication of these units, the term " miles per hour " is not normally used in the natural sciences.

As a non- metric unit miles per hour (mph ) is used mainly in the U.S. and some other English speaking countries. In the maritime and aviation also the unit node (kn) is in use. A knot is one nautical mile ( nm) per hour. Vertical velocities in powered aviation are often in feet per minute ( LFM of Engl. Linear feet per minute) specified.

Almost exclusively in the aviation the Mach is used which is not an absolute quantity, but is the ratio of the velocity to the local speed of sound. The sound velocity is strongly temperature-dependent but non-air- pressure-dependent. The reason for the use of this number is that aerodynamic effects depend on it.

Conversion of common units of velocity:

## Tangential and radial velocity

The radial velocity refers to the component of a velocity vector along the line connecting the moving object and the origin of coordinates. Vertically it is the vector for the tangential ( circumferential speed also ). This results in:

The vector product of the angular velocity and the tangential velocity of the position vector results.

From the change of the distance to the origin of coordinates (radius) the radial velocity follows.

## Absolute, relative and execution speed

It is an arbitrary inertial system adopted from which a body is observed. In this reference system the body moves with absolute velocity. Now is added a moving reference system. There, the body has a relative speed and the speed of the moving reference frame is called transfer speed.

For a better presentation of the facts is an example: When ( approximately) inertial observer is a waiting passenger in the train station, the moving frame is a by -propelled train is and the moving body is the conductor that runs through the train.

For astronomy, the absolute speed plays no role, because in principle there is no absolute reference system at rest. The coordinate axes have a fixed orientation to the fixed stars and the reference system rests in the respective barycenter. For example, the velocity of the Moon:

For distant objects in the universe, the speed is determined primarily by the expansion of space-time, and is measured as the redshift. Therefore, in astronomy ( Earth-Moon system, the solar system, Earth orbit of a satellite ) or to the observation plays only the display of the relative velocity with respect to a selected Gravizentrum a role.

## Speed of many particles

The velocities in a flowing medium can be regarded as a vector field.

## Relativity theory

As long as the velocity of an observed object has a significantly smaller value than the speed of light, the laws of classical mechanics apply to a good approximation. More detailed considerations require the observance of the special theory of relativity.

## Historical Note

Galileo Galilei well defined first the speed - uniform rectilinear motion geometrically, as a proportionality between the distance traveled by the moving body stretches s at the times required for this t. This is equivalent in today's terms of average speed.