Speed and Velocity: Difference between revisions

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[[File:Speed.JPG]]
[[File:Speed.JPG]]


=Simple Example=
=Simple Examples=
[[File:pathindependence.png]]
1. If a person walked a distance of 10 meters in 5 seconds, what is their average velocity?


In this example, the electric field is equal to <math> E = \left(E_x, 0, 0\right)</math>. The initial location is A and the final location is C. In order to find the potential difference between A and C, we use <math>dV = V_C - V_A </math>.  
Solution: Using the average velocity equation will tell you that the answer is 2 m/s.


Since there are no y and z components of the electric field, the potential difference is <math> dV = -\left(E_x*\left(x_1 - 0\right) + 0*\left(-y_1 - 0\right) + 0*0\right)  = -E_x*x_1</math>
2. If someone traveled with a velocity of 13 m/s for 3 minutes, how far would they have traveled?


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


Let's say there is a location B at <math> \left(x_1, 0, 0\right) </math>. Now in order to find the potential difference between A and C, we need to find the potential difference between A and B and then between B and C.
The potential difference between A and B is <math>dV = V_B - V_A = -\left(E_x*\left(x_1 - 0\right) + 0*0 + 0*0\right) = -E_x*x_1</math>.
The potential difference between B and C is <math>dV = V_C - V_B = -\left(E_x*0 + 0*\left(-y_1 - 0\right) + 0*0\right) = 0</math>.
Therefore, the potential difference A and C is <math>V_C - V_A = \left(V_C - V_B\right) + \left(V_B - V_A\right) = E_x*x_1 </math>, which is the same answer that we got when we did not use location B.


==Connectedness==
==Connectedness==
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#How is it connected to your major?
#How is it connected to your major?
#Is there an interesting industrial application?
#Is there an interesting industrial application?
==History==
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.


== See also ==
== See also ==

Revision as of 15:05, 30 November 2015

by Matt Schoonover

Speed and Velocity

Speed and velocity are used fairly interchangeably in casual conversation, but when it comes to physics the two can mean vastly different things. Velocity has direction and therefor a vector quantity. Speed is the scalar form of velocity and therefor has no direction.

The most basic equation for velocity is

From this comes the average velocity equation of

The equation for speed is

A Mathematical Model

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

To help demonstrate the difference between the two, I wrote 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.


Connectedness

  1. How is this topic connected to something that you are interested in?
  2. How is it connected to your major?
  3. Is there an interesting industrial application?

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

Internet resources on this topic

References

This section contains the the references you used while writing this page

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