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==Speed and Velocity==
==Speed and Velocity==


Speed and velocity are used fairly interchangeably in casual conversation, but when it comes to physics the two can mean different things. First off, velocity is a vector quantity, which means it contains a directional component that speed doesn't have.  
Speed and velocity are used fairly interchangeably in casual conversation, but when it comes to physics the two can mean different things. First off, velocity is a vector quantity, which means it contains a directional component that speed doesn't have. Speed is defined as distance over time, but velocity is displacement over time. Displacement is the final position of an object minus the initial position of the object, sometimes referred to as the origin.  Displacement is shown by the vector quantity ''r''.


The most basic equation for velocity is
[[File:veq.JPG]]


From this comes the average velocity equation of  
===A Mathematical Model===
[[File:velocity1.JPG]]
 
 
The most basic equation for velocity is:
 
[[File:Velocity2.png]]
 
where the arrow on top of the ''r'' shows that it is a vector. As you recall, a vector divided by a scalar is still a vector, giving us velocity.
 
In order to covert this vector quantity, velocity, to its corresponding scalar, speed, you can take the magnitude of the quantity.
 
[[File:Speedeq.JPG]]


The equation for speed is  
Finding the displacement of an object given the speed and velocity is simple. Since speed is the magnitude of velocity, you can use speed to find the unit vector.
[[File:velocity2.JPG]]


===A Mathematical Model===
[[File:uniteq.JPG]]


In order to find the velocity of an object one must find the change in distance over the change in time. In order to find the speed of an object one must find the magnitude of the velocity. Both are measured in meters per second.


===A Computational Model===
===A Computational Model===


To help demonstrate the difference between the two, I wrote some simple code to model the motion of a ball moving on a track.
To help demonstrate the difference between the two, here is some simple code to model the motion of a ball moving on a track.


In the first picture, the velocity is only in one direction, so the speed and velocity are the same.
In the first picture, the velocity is only in one direction, so the speed and velocity are the same.
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[[File:Speed.JPG]]
[[File:Speed.JPG]]


==Unit Vectors==
Unit vectors are also closely related to velocity and speed. Basically a unit vector is a unitless vector with a magnitude of 1 unit that points in the direction of a given vector. Unit vectors can be used to switch between speed and velocity.
The equation to find the unit vector of velocity is simply velocity over speed, or
[[File:uniteq.JPG]]
Multiplying the speed by a unit vector will give you velocity.


=Simple Examples=
=Simple Examples=
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Solution: 5 m/s * <3,2,1> = <15,10,5> m/s
Solution: 5 m/s * <3,2,1> = <15,10,5> m/s




Revision as of 16:12, 17 April 2016

by Matt Schoonover edited by Gautami Chennur

Speed and Velocity

Speed and velocity are used fairly interchangeably in casual conversation, but when it comes to physics the two can mean different things. First off, velocity is a vector quantity, which means it contains a directional component that speed doesn't have. Speed is defined as distance over time, but velocity is displacement over time. Displacement is the final position of an object minus the initial position of the object, sometimes referred to as the origin. Displacement is shown by the vector quantity r.


A Mathematical Model

The most basic equation for velocity is:

where the arrow on top of the r shows that it is a vector. As you recall, a vector divided by a scalar is still a vector, giving us velocity.

In order to covert this vector quantity, velocity, to its corresponding scalar, speed, you can take the magnitude of the quantity.

Finding the displacement of an object given the speed and velocity is simple. Since speed is the magnitude of velocity, you can use speed to find the unit vector.


A Computational Model

To help demonstrate the difference between the two, here is some simple code to model the motion of a ball moving on a track.

In the first picture, the velocity is only in one direction, so the speed and velocity are the same.


However, in the second picture, the velocity is in the x and y direction, so the speed and velocity are not the same.


Simple Examples

1. If a person walked a distance of 10 meters in 5 seconds, what is their average velocity?

Solution: Using the average velocity equation will tell you that the answer is 2 m/s.

2. If someone traveled with a velocity of 13 m/s for 3 minutes, how far would they have traveled?

Solution: First convert 3 minutes to seconds(180). Then use the velocity equation to solve for distance. You should get 2,340 m.

3. What is the unit vector for the velocity vector <3,4,0> m/s?

Solution: Use the speed equation to get that the speed is 5 and the unit vector equation to get a final answer of <3/5,4/5,0>

4. What is the velocity of an object if the unit vector is <3,2,1> and the speed is 5 m/s?

Solution: 5 m/s * <3,2,1> = <15,10,5> m/s


See also


External links

  • A physics resource written by experts for an expert audience Physics Portal
  • A wiki book on modern physics Modern Physics Wiki
  • The MIT open courseware for intro physics MITOCW Wiki
  • An online concept map of intro physics HyperPhysics
  • Interactive physics simulations PhET
  • OpenStax algebra based intro physics textbook College Physics
  • The Open Source Physics project is a collection of online physics resources OSP
  • A resource guide compiled by the AAPT for educators ComPADRE

References

Matter and Interactions, Modern Mechanics, Volume One 4th Edition by Chabay and Sherwood.

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