velocity

American Heritage Dictionary:

ve·loc·i·ty

(və-lŏs'ĭ-tē) pronunciation

n., pl., -ties.

Rapidity or speed of motion; swiftness.
Physics. A vector quantity whose magnitude is a body's speed and whose direction is the body's direction of motion.
1. The rate of speed of action or occurrence.
2. The rate at which money changes hands in an economy.

[Middle English velocite, from Old French, from Latin vēlōcitās, from vēlōx, vēlōc-, fast.]

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velocity

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Quantity that designates the speed and direction in which a body moves. It can be represented graphically by an arrow (pointing in the direction of the motion), the length of which is proportional to the magnitude, or speed. For an object in circular motion, the direction at any instant is tangential to the circle at that point, and so is perpendicular to the radius at that point. The instantaneous speed of a vehicle, such as an automobile, can be determined by a speedometer, or mathematically by differential calculus. The average speed is the ratio of the distance traveled in any given time interval divided by the time taken.

For more information on velocity, visit Britannica.com.

McGraw-Hill Science & Technology Encyclopedia:

Velocity

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The time rate of change of position of a body in a particular direction. Linear velocity is velocity along a straight line, and its magnitude is commonly measured in such units as meters per second (m/s), feet per second (ft/s), and miles per hour (mi/h). Since both a magnitude and a direction are implied in a measurement of velocity, velocity is a directed or vector quantity, and to specify a velocity completely, the direction must always be given. The magnitude only is called the speed. See also Speed.

A body need not move in a straight line path to possess linear velocity. When a body is constrained to move along a curved path, it possesses at any point an instantaneous linear velocity in the direction of the tangent to the curve at that point. The average value of the linear velocity is defined as the ratio of the displacement to the elapsed time interval during which the displacement took place.

Angular velocity shown as an axial vector. Axis of rotation is OO ^′.

The representation of angular velocity ω as a vector is shown in the illustration. The vector is taken along the axis of spin. Its length is proportional to the angular speed and its direction is that in which a right-hand screw would move. If a body rotates simultaneously about two or more rectangular axes, the resultant angular velocity is the vector sum of the individual angular velocities.

Barron's Finance & Investment Dictionary:

velocity

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rate of spending, or turnover of money—in other words, how many times a dollar is spent in a given period of time. The more money turns over, the faster velocity is said to be. The concept of “income velocity of money” was first explained by the economist Irving Fisher in the 1920s as bearing a direct relationship to gross domestic product (GDP). Velocity usually is measured as the ratio of GDP to the money supply. Velocity affects the amount of economic activity generated by a given money supply, which includes bank deposits and cash in circulation. Velocity is a factor in the Federal Reserve Board’s management of monetary policy, because an increase in velocity may obviate the need for a stimulative increase in the money supply. Conversely, a decline in velocity might reflect dampened economic growth, even if the money supply holds steady.
See also fiscal policy.

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Roget's Thesaurus:

velocity

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noun

Informal

See

Oxford Dictionary of Sports Science & Medicine:

linear velocity

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Rate at which a body moves in a straight line from one location to another. Average linear velocity = displacement/time taken. The linear velocity of a point on a turning body, such as a lever, is directly proportional to its distance from the axis. Therefore, the maximum linear velocity of a moving lever (such as a limb) occurs at its distal end, and the longer the radius of the lever, the greater its linear velocity.

Columbia Encyclopedia:

velocity

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velocity, change in displacement with respect to time. Displacement is the vector counterpart of distance, having both magnitude and direction. Velocity is therefore also a vector quantity. The magnitude of velocity is known as the speed of a body. The average velocity or average speed of a moving body during a time period t may be computed by dividing the total displacement or total distance by t. Computation of the instantaneous velocity at a particular moment, however, usually requires the methods of the calculus.

Word Tutor:

velocity

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IN BRIEF: Rate of motion.

A lot more electricity is produced if the turbines spin with a greater velocity.

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Dictionary of Cultural Literacy: Science:

velocity

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The vector giving the speed and direction of motion of any object.

McGraw-Hill Dictionary of Aviation:

velocity

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The rate of change of position in a given direction.

Random House Word Menu:

categories related to 'velocity'

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Random House Word Menu by Stephen Glazier

For a list of words related to velocity, see:

Principles of Mechanics, Waves, and Measurement - velocity: rate of change of position in particular direction
Aviation and Aerodynamics - velocity: rate of motion in particular direction
Baseball - velocity: the speed of a pitch

Rhymes:

velocity

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See words rhyming with "velocity."

Bradford's Crossword Solver's Dictionary:

velocity

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See crossword solutions for the clue Velocity.

Wikipedia on Answers.com:

Velocity

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This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2011)

This article is about velocity in physics. For other uses, see Velocity (disambiguation).

Classical mechanics
$\mathbf{F} = m \mathbf{a}$ Newton's Second Law
History of classical mechanics · Timeline of classical mechanics
Branches Statics · Dynamics / Kinetics · Kinematics · Applied mechanics · Celestial mechanics · Continuum mechanics · Statistical mechanics
Formulations Newtonian mechanics (Vectorial mechanics) Analytical mechanics: Lagrangian mechanics Hamiltonian mechanics
Fundamental concepts Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle
Core topics Rigid body · Rigid body dynamics · Euler's equations (rigid body dynamics) · Motion · Newton's laws of motion · Newton's law of universal gravitation · Euler's laws of motion · Equations of motion · Inertial frame of reference · Non-inertial reference frame · Rotating reference frame · Fictitious force · Linear motion · Mechanics of planar particle motion · Displacement (vector) · Relative velocity · Friction · Simple harmonic motion · Harmonic oscillator · Vibration · Damping · Damping ratio · Rotational motion · Circular motion · Uniform circular motion · Non-uniform circular motion · Centripetal force · Centrifugal force · Centrifugal force (rotating reference frame) · Reactive centrifugal force · Coriolis force · Pendulum · Rotational speed · Angular acceleration · Angular velocity · Angular frequency · Angular displacement
Scientists Galileo Galilei · Isaac Newton · Jeremiah Horrocks · Leonhard Euler · Jean le Rond d'Alembert · Alexis Clairaut · Joseph Louis Lagrange · Pierre-Simon Laplace · William Rowan Hamilton · Siméon-Denis Poisson
v d e

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant direction typically constrains the object to motion in a straight path. A car moving at a constant 20 kilometers per hour in a circular path does not have a constant velocity. The rate of change in velocity is acceleration. Velocity is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed, a quantity that is measured in metres per second (m/s or ms⁻¹) when using the SI (metric) system.

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 $( \Delta \mathbf{d})$ during a time interval $(Δ t)$ is described by the formula:

$\mathbf{\bar{v}} = \frac{\Delta \mathbf{d}}{\Delta t}.$

The rate of change of velocity (in m/s) as a function of time (in s) is acceleration (in m/s²) – how an object's speed or direction of travel changes over time, and how it is changing at a particular point in time.

Contents

1 Equation of motion
2 Relative velocity
- 2.1 Scalar velocities
3 Polar coordinates
4 See also
5 References
6 External links

Equation of motion

Main article: Equation of motion

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

$\mathbf{v} = \lim_{\Delta t \to 0}{{\mathbf{x}(t+\Delta t)-\mathbf{x}(t)} \over \Delta t}={\mathrm{d}\mathbf{x} \over \mathrm{d}t}.$

Average velocity magnitudes always smaller than or equal to average speed of a given particle. Instantaneous velocity is always tangential to trajectory. Slope of tangent of position or displacement time graph is instantaneous velocity and its slope of chord is average velocity.

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 $Δ t$ is:

$\mathbf{v} = \mathbf{u} + \mathbf{a} \Delta t.$

The average velocity of an object undergoing constant acceleration is $\tfrac {(\mathbf{u} + \mathbf{v})}{2}$ , where u is the initial velocity and v is the final velocity. To find the position, x, of such an accelerating object during a time interval, $Δ t$ , then:

$\Delta \mathbf{x} = \frac {( \mathbf{u} + \mathbf{v} )}{2}\Delta t.$

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

$\Delta \mathbf{x} = \mathbf{u} \Delta t + \frac{1}{2}\mathbf{a} \Delta t^2,$

can be used.

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

$\mathbf{x}(t) = \mathbf{x}(0) + \Delta \mathbf{x} = \mathbf{x}(0) + \mathbf{u} \Delta t + \frac{1}{2}\mathbf{a} \Delta t^2,$

These basic equations for final velocity and position 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), $E K$ , of a moving object is linear with both its mass and the square of its velocity:

$E_{K} = \begin{matrix} \frac{1}{2} \end{matrix} mv^2.$

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 the Earth's surface is approximately 11100 m/s.

Relative velocity

Main article: 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:

$\mathbf{v}_{A\text{ relative to }B} = \mathbf{v} - \mathbf{w}$

Similarly the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is:

$\mathbf{v}_{B\text{ relative to }A} = \mathbf{w} - \mathbf{v}$

Usually the inertial frame is chosen in which the latter of the two mentioned objects is in rest.

Scalar velocities

In the one dimensional case,^[1] the velocities are scalars and the equation is either:

$\, v_{rel} = v - (-w)$ , if the two objects are moving in opposite directions, or:

$\, v_{rel} = v -(+w)$ , 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.

$\mathbf{v}=\mathbf{v}_T+\mathbf{v}_R$

where

$\mathbf{v}_T$ is the transverse velocity

$\mathbf{v}_R$ is the radial velocity.

The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.

$v_R=\frac{\mathbf{v} \cdot \mathbf{r}}{\left|\mathbf{r}\right|}$

where

$\mathbf{r}$ is displacement.

The magnitude of the transverse velocity is that of the cross product of the unit vector in the direction of the displacement and the velocity vector. It is also the product of the angular speed $ω$ and the magnitude of the displacement.

$v_T=\frac{|\mathbf{r}\times\mathbf{v}|}{|\mathbf{r}|}=\omega|\mathbf{r}|$

such that

$\omega=\frac{|\mathbf{r}\times\mathbf{v}|}{|\mathbf{r}|^2}.$

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.

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

where

$m\,$ is mass

$r=\|\mathbf{r}\|.$

The expression $m r 2$ is known as moment of inertia. 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.

References

^ Basic principle

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

External links

Physicsclassroom.com, Speed and Velocity
Introduction to Mechanisms (Carnegie Mellon University)

v d e Kinematics

← Integrate … Differentiate → Displacement (Distance) \| Velocity (Speed) \| Acceleration \| Jerk \| Jounce

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Translations:

Velocity

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Dansk (Danish)
n. - hastighed

Nederlands (Dutch)
snelheid, omzetsnelheid

Français (French)
n. - (Tech) vitesse, vélocité

Deutsch (German)
n. - Geschwindigkeit

Ελληνική (Greek)
n. - ταχύτητα

Italiano (Italian)
velocitý

Português (Portuguese)
n. - velocidade (f)

Русский (Russian)
скорость, быстрота

Español (Spanish)
n. - velocidad, rapidez

Svenska (Swedish)
n. - hastighet, snabbhet

中文（简体）(Chinese (Simplified))
速度, 迅速, 速率

中文（繁體）(Chinese (Traditional))
n. - 速度, 迅速, 速率

한국어 (Korean)
n. - 속도, 빠르기, 속력

日本語 (Japanese)
n. - 速度, 高速

العربيه (Arabic)
‏(الاسم) سرعه‏

עברית (Hebrew)
n. - ‮מהירות‬

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