Velocity Measure

A Velocity Measure is a physical object measure of the rate of change of physical distance traveled with respect to time.

• AKA: Instantaneous Velocity.
• Context:
  • It is a vector quantity and its magnitude (i.e vector norm) is usually called speed.
  • It can be defined as the derivative of distance ([math]\displaystyle{ \vec{s} }[/math]) with respect to time [math]\displaystyle{ \vec{v}=d\vec{s}/dt }[/math].

• The units of measurement of velocity are given by:

[math]\displaystyle{ [velocity]=\frac{[distance]}{[time]}=\frac{[length]}{[time]} }[/math]

where [math]\displaystyle{ [x] }[/math] symbolizes the conversion of the quantity [math]\displaystyle{ x }[/math] to its units of measurement. Thus, the units of measurement for acceleration can be given in meters per seconds, [math]\displaystyle{ m/s }[/math], (in International System of Units or metric system) or feet per seconds (imperial system).

• On average the velocity can be estimated to be:

[math]\displaystyle{ \vec{v}_{average}=\vec{\bar{v}}=\frac{\Delta s}{\Delta t}=\frac{\vec{s_2}-\vec{s_1}}{t_2-t_1} }[/math]

• It can also be defined as the integral of the acceleration [math]\displaystyle{ \vec{v}=\int\vec{a}\;dt }[/math].
• There is direct proportionality of velocity to momentum and the inverse proportionality of velocity to mass

[math]\displaystyle{ \vec{p} =m\vec{v} \quad\iff\quad \vec{v}=\frac{\vec{p}}{m} }[/math]

(Note: this is assuming object's mass is a constant, relativistic effects have to be taken into account when the object approches the speed of light).

• Example(s)
  • Speed.
  • Muzzle velocity.
  • Angular Velocity.
  • Escape Velocity.
  • Velocity of Sound.
  • Friction Velocity.
• Counter-Example(s)
  • Acceleration.
  • Distance.
  • Time.
  • Momentum
• See: Acceleration, Meter, Second, Time Derivative, Position (Vector), Frame of Reference, Speed, Kinematics, Classical Mechanics, Motion (Physics), Vector (Geometry), Physical Quantity, Muzzle velocity, Angular Velocity, Escape Velocity, Velocity of Sound, Friction Velocity, Distance, Momentum.

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References

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/velocity Retrieved:2016-4-29.
  • The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion (e.g. to the north). Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

    Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric) system as metres per second (m/s) or as the SI base unit of (m⋅s⁻¹). For example, "5 metres per second" is a scalar (not a vector), whereas "5 metres per second east" is a vector.

    If there is a change in speed, direction, or both, then the object has a changing velocity and is said to be undergoing an acceleration.

2005

• (Hyperphysics Encyclopedia, 2005) ⇒ http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html#c1
  • QUOTE: The average speed of an object is defined as the distance traveled divided by the time elapsed. Velocity is a vector quantity, and average velocity can be defined as the displacement divided by the time. For the special case of straight line motion in the x direction, the average velocity takes the form:

[math]\displaystyle{ \vec{v}_{average}=\vec{\bar{v}}=\frac{\Delta x}{\Delta t}=\frac{\vec{x_2}-\vec{x_1}}{t_2-t_1} }[/math]

The units for velocity can be implied from the definition to be meters/second or in general any distance unit over any time unit.

[math]\displaystyle{ \vec{v}_{instantaneous}=\lim_{\Delta\;t\rightarrow\;0}\frac{\Delta \vec{x}}{\Delta t}=\frac{d\vec{x}}{dt} }[/math]

You can approach an expression for the instantaneous velocity at any point on the path by taking the limit as the time interval gets smaller and smaller. Such a limiting process is called a derivative and the instantaneous velocity can be defined as

1963

• (Feynman et al., 1963) ⇒ Richard P. Feynman, Robert B. Leighton and Matthew Sands (1963, 1977, 2006, 2010, 2013) "The Feynman Lectures on Physics": New Millennium Edition is now available online by the California Institute of Technology, Michael A. Gottlieb, and Rudolf Pfeiffer ⇒ http://www.feynmanlectures.caltech.edu/
  • See: Chapter 8 ⇒ http://www.feynmanlectures.caltech.edu/I_08.html

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