## Speed

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The speed ( symbols : v, 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 amount indicates which path traveled by a point of a body within a certain period of time. Figures refer to the amount of the vector quantity, this is for example the speedometer displayed a car. The international unit used for speed is meters per second (m / s) , is also commonly used kilometers per hour (km / h) .

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

Generalizes the term velocity change of a physical size over time (see the rate of change ).

Contents

Etymology

Geschwind (adjective of 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, evil, dangerous’. Old High German presence is demonstrated by names like Amalswind, Swindbert, Swinda. [1]

Definition

Trajectory and distance

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

\ Bar {v} = \ frac {s \ left (t \ right)} {t}

A section s Δ between the points P 1 and P 2, the period of time Δ t required. This results in the average speed is in the examined section.

\ Bar {v} _ {\ Delta s} = \ frac {s \ left ({t} _ {2} \ right)-s \ left ({t} _ {1} \ right)} {{t} _ {2} – {t} _ {1}} = \ frac {\ Delta s} {\ Delta t}

By reducing the observation period Δ t to a vanishingly small time interval creates a limit to mathematics as differential quotients knows or derivative of the distance with respect to time. As a result, the instantaneous velocity.

v = \ underset {\ Delta t \ rightarrow 0} {\ lim} \ frac {\ Delta s} {\ Delta t} = \ frac {\ text {d} s} {\ text {d} t} = \ dot {s}

Position vector and distance

A movement in the room has a course which is called trajectory and the description of the position vector {\ Bf r} \ left (t \ right) as function of time takes place. Since any change in the location one direction which is also the speed which characterizes this change in relation to time, represents a vector quantity

{\ Bf v} = \ underset {\ Delta t \ rightarrow 0} {\ lim} \ frac {\ Delta {\ bf r}} {\ Delta t} = \ frac {\ text {d} {\ bf r} } {\ text {d} t} = \ dot {\ bf r}

acceleration and jerk

The derivative of the velocity with respect to time is the acceleration : \ Frac {a} (t) = \ frac {\ vec {v}} (t)

The second derivative of the velocity with respect to time gives the jerk movement: \ Frac {j} (t) = \ ddot {\ bf {v}} (t)

Units

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

In everyday language, is also the term ” miles per hour “is used. As in physics, such a composition of two units (here: “Hour” and “miles”) is understood as a multiplication of these units, the term “miles per hour” to be avoided.

As a non-metric unit, especially in the U.S. and some other is English speaking countries miles per hour ( mph ) is used. In the maritime and aviation unit is also the knots (kn) in use. A knot is one nautical mile (nm) per hour. Vertical velocities in the powered flight are often in foot per minute (LFM of English. linear feet per minute) indicated.

Almost exclusively in aviation is the Mach used that has no absolute value, but the ratio of the speed to the local speed of sound indicates. The speed of sound is strongly dependent on temperature but air pressure dependent . The reason for the use of this number is that aerodynamic effects depend on it.

Conversion of Common Unit speed:

1 knot = 1 nautical mile / h = 0.5144 m / s = 1.852 km / h;

1 m / s = 3.6 km / h (exactly) = 1.944 kn = 2.237 mph;

1 km / h = 0.2778 m / s = 0,540 kn = 0.6214 mph;

1 mph = 0.8690 kn = 0.44704 m / s (exact) = 1.609344 km / h (exactly);

100 ft / min = 0.508 m / s (exact);

c = 299,792,458 m / s (exact) = 1079252848.8 km / h (exact).

tangential and radial velocity

Gone flying aircraft with speed (red), radial velocity (green) and tangential (blue)

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

\ Vec v = {\ bf v} _ {\ perp} + {\ bf v} _ \ mathrm {r}

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

{\ Bf v} _ {\ perp} = \ vec \ omega \ times \ vec r

From the change of the distance to the origin (radius) followed by the radial velocity.

| {\ Bf v} _ \ mathrm {r} | = \ frac {r}

See also: web speed (Astronomy)

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 speed. Now added a moving reference frame. There, the body has a relative speed and the speed of the moving reference frame is called the operating speed.

\ Vec v_ \ mathrm {a} = \ vec v_ \ mathrm {r} + \ vec v_ \ mathrm {f}

For a better idea of the situation is an example: When (approximately) inertial observers there is a waiting passenger at the station, the moving reference system represents through moving train and the moving body is the conductor that runs through the train.

Relative velocity in astronomy

For astronomy plays no role, absolute speed, because in principle there is no absolute reference frame 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 speed of the moon:

Velocity of the moon Mean orbital velocity

(Around the Earth-Moon gravity ) around the sun / barycenter of the solar system around the galactic center relative to Andromeda

Speed in km / s 1.02 ± 5.5% mensal 29.78 ± 1.51 (± 5.1% annual) ~ 250

(Depending galactic year unknown, precise fluctuations) 266 ± 31.3 (annual)

Proportion of the average path speed at the middle relative velocity in percent 100% 3.4% 0.4% 0.37%

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

Speed of many particles

The speeds in a flowing medium have the vector field can be perceived.

See also: flow field

Theory of Relativity

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

| \ Vec v | \ ll c

Historical Note

Galileo Galilei , the first well-defined speed-uniform rectilinear motion geometrically, as a proportionality of the moving body covered s routes to their required time t. [2] This is in today’s terms of average speed.