# Dictionary Definition

velocity n : distance travelled per unit time
[syn: speed]

# User Contributed Dictionary

## English

### Noun

velocity#### Translations

vector quantity

rapidity of motion

##### Translations to be checked

# Extensive Definition

In physics, velocity is defined as
the rate of
change of position.
It is a vector
physical
quantity; both speed and direction are required to define it.
In the
SI (metric) system, it is measured in metres per
second: (m/s) or ms-1. The scalar
absolute
value (magnitude)
of velocity is speed. For
example, "5 metres per second" is a scalar
and not a vector, whereas "5 metres per second east" is a vector.
The average velocity v of an object moving through a displacement (
\Delta \mathbf) during a time interval ( \Delta t) is described by
the formula:

- \bar = \frac.

The rate of change of velocity is referred to as
acceleration.

## Equation of motion

The instant velocity vector \, v of an object
that has positions \, x(t) at time \, t and \, x(t + ) at time \, t
+, can be computed as the derivative of position:

- \, \mathbf = \lim_=

The equation for an object's velocity can be
obtained mathematically by evaluating the integral of the equation for
its acceleration beginning from some initial period time \, t_0 to
some point in time later \, t_n.

The final velocity v of an object which starts
with velocity u and then accelerates at constant acceleration a for
a period of time \, ( \Delta t) is:

- \mathbf = \mathbf + \mathbf \Delta t

The average velocity of an object undergoing
constant acceleration is \begin
\frac \; \end, where u is the initial velocity and v is the final
velocity. To find the displacement, x, of such an accelerating
object during a time interval, \Delta t, then:

- \Delta \mathbf = \frac \Delta t

When only the object's initial velocity is known,
the expression,

- \Delta \mathbf = \mathbf \Delta t + \frac\mathbf \Delta t^2,

can be used.

This can be expanded to give the position at any
time t in the following way:

- \mathbf(t) = \mathbf(0) + \Delta \mathbf = \mathbf(0) + \mathbf \Delta t + \frac\mathbf \Delta t^2,

These basic equations for final velocity and
displacement can be combined to form an equation that is
independent of time, also known as Torricelli's
equation:

- v^2 = u^2 + 2a\Delta x.\,

The above equations are valid for both Newtonian
mechanics and special
relativity. Where Newtonian mechanics and special relativity
differ is in how different observers would describe the same
situation. In particular, in Newtonian mechanics, all observers
agree on the value of t and the transformation rules for position
create a situation in which all non-accelerating observers would
describe the acceleration of an object with the same values.
Neither is true for special relativity. In other words only
relative
velocity can be calculated.

In Newtonian mechanics, the kinetic
energy (energy of
motion), \, E_, of a moving object is linear with both its mass and the square of its
velocity:

- E_ = \begin \frac \end mv^2.

The kinetic energy is a scalar
quantity.

Escape
velocity is the minimum velocity a body must have in order to
escape from the gravitational field of the earth. To escape from
the earth's gravitational field an object must have greater kinetic
energy than its gravitational potential energy. The value of the
escape velocity from Earth is approximately 11100 m/s

## Relative velocity

Relative velocity is a measurement of velocity
between two objects as determined in a single coordinate system.
Relative velocity is fundamental in both classical and modern
physics, since many systems in physics deal with the relative
motion of two or more particles. In Newtonian mechanics, the
relative velocity is independent of the chosen inertial reference
frame. This is not the case anymore with special
relativity in which velocities depend on the choice of
reference frame.

If an object A is moving with velocity vector v
and an object B with velocity vector w , then the velocity of
object A relative to object B is defined as the difference of the
two velocity vectors:

- \mathbf_ = \mathbf - \mathbf

- \mathbf_ = \mathbf - \mathbf

### Scalar velocities

In the one dimensional case, the velocities are scalars and the equation is either:- \, v_ = v - (-w), if the two objects are moving in opposite directions, or:
- \, v_ = v -(+w), if the two objects are moving in the same direction.

## Polar coordinates

In polar coordinates, a two-dimensional velocity is described by a radial velocity, defined as the component of velocity away from or toward the origin (also known as velocity made good), and an angular velocity, which is the rate of rotation about the origin (with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system).The radial and angular velocities can be derived
from the Cartesian velocity and displacement vectors by decomposing
the velocity vector into radial and transverse components. The
transverse velocity
is the component of velocity along a circle centered at the
origin.

- \mathbf=\mathbf_T+\mathbf_R

- \mathbf_T is the transverse velocity
- \mathbf_R is the radial velocity

- v_R=\frac

- \mathbf is displacement

- v_T=\frac=\omega|\mathbf|

- \omega=\frac

Angular
momentum in scalar form is the mass times the distance to the
origin times the transverse velocity, or equivalently, the mass
times the distance squared times the angular speed. The sign
convention for angular momentum is the same as that for angular
velocity.

- L=mrv_T=mr^2\omega\,

- m\, is mass
- r=|\mathbf|

If forces are in the radial direction only with
an inverse square dependence, as in the case of a gravitational
orbit, angular momentum is
constant, and transverse speed is inversely proportional to the
distance, angular speed is inversely proportional to the distance
squared, and the rate at which area is swept out is constant. These
relations are known as
Kepler's laws of planetary motion

## See also

- Kinematics
- Relative velocity
- Terminal velocity
- Hypervelocity
- Four-velocity (relativistic version of velocity for Minkowski spacetime)
- Rapidity (a version of velocity additive at relativistic speeds)
- Proper velocity (in relativity, using traveler time instead of observer time)

## References

- Halliday, David, Robert Resnick and Jearl Walker, Fundamentals of Physics, Wiley; 7 Sub edition (June 16, 2004). ISBN 0471232319.

## External links

- Speed and Velocity (The Physics Classroom)
- Introduction to Mechanisms (Carnegie Mellon University)

velocity in Arabic: سرعة (ميكانيكا)

velocity in Min Nan: Sok-tō͘

velocity in Bulgarian: Скорост

velocity in Bosnian: Brzina

velocity in Catalan: Velocitat

velocity in Czech: Rychlost

velocity in Danish: Hastighed

velocity in German: Geschwindigkeit

velocity in Esperanto: Vektora rapido

velocity in Spanish: Velocidad

velocity in Basque: Abiadura

velocity in Persian: سرعت

velocity in Finnish: Nopeus

velocity in French: Vitesse

velocity in Hebrew: מהירות

velocity in Hindi: वेग

velocity in Hungarian: Sebesség

velocity in Korean: 속도

velocity in Icelandic: Hraði

velocity in Italian: Velocità

velocity in Japanese: 速度

velocity in Korean: 속도

velocity in Latin: Velocitas

velocity in Malay (macrolanguage): Halaju

velocity in Dutch: Snelheid

velocity in Polish: Prędkość

velocity in Portuguese: Velocidade

velocity in Quechua: Utqa kay

velocity in Russian: Скорость

velocity in Simple English: Velocity

velocity in Slovenian: Hitrost

velocity in Swedish: Hastighet

velocity in Thai: ความเร็ว

velocity in Turkish: Hız

velocity in Vietnamese: Vận tốc

velocity in Ukrainian: Швидкість

velocity in Urdu: سمتار

velocity in Chinese: 速度

# Synonyms, Antonyms and Related Words

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