## English

### Noun

velocities- Plural of velocity

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 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

- \, 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.

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

- 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)

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

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

velocities in Arabic: سرعة (ميكانيكا)

velocities in Min Nan: Sok-tō͘

velocities in Bulgarian: Скорост

velocities in Bosnian: Brzina

velocities in Catalan: Velocitat

velocities in Czech: Rychlost

velocities in Danish: Hastighed

velocities in German: Geschwindigkeit

velocities in Esperanto: Vektora rapido

velocities in Spanish: Velocidad

velocities in Basque: Abiadura

velocities in Persian: سرعت

velocities in Finnish: Nopeus

velocities in French: Vitesse

velocities in Hebrew: מהירות

velocities in Hindi: वेग

velocities in Hungarian: Sebesség

velocities in Korean: 속도

velocities in Icelandic: Hraði

velocities in Italian: Velocità

velocities in Japanese: 速度

velocities in Korean: 속도

velocities in Latin: Velocitas

velocities in Malay (macrolanguage):
Halaju

velocities in Dutch: Snelheid

velocities in Polish: Prędkość

velocities in Portuguese: Velocidade

velocities in Quechua: Utqa kay

velocities in Russian: Скорость

velocities in Simple English: Velocity

velocities in Slovenian: Hitrost

velocities in Swedish: Hastighet

velocities in Thai: ความเร็ว

velocities in Turkish: Hız

velocities in Vietnamese: Vận tốc

velocities in Ukrainian: Швидкість

velocities in Urdu: سمتار

velocities in Chinese: 速度

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