Speed vs Velocity: Difference between revisions
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==Average Speed vs Average Velocity== | ==Average Speed vs Average Velocity== | ||
One of the biggest sources of confusion between speed and velocity is between average speed and average velocity. This is because although instantaneous speed is the magnitude of instantaneous velocity, average speed may not be the magnitude of average velocity. To understand why, let us take a look at the following formulas: | One of the biggest sources of confusion between speed and velocity is the difference between average speed and average velocity. This is because although instantaneous speed is the magnitude of instantaneous velocity, average speed may not be the magnitude of average velocity. To understand why, let us take a look at the following formulas: | ||
<math>\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}</math> | <math>\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}</math> | ||
where <math>\Delta \vec{r}</math> is the change in position over that time interval (<math>\Delta \vec{r} = \vec{r}_f - \vec{r}_i</math>). | where <math>\Delta \vec{r}</math> is the displacement (change in position) over that time interval (<math>\Delta \vec{r} = \vec{r}_f - \vec{r}_i</math>). | ||
<math>v_{avg} = \frac{\Delta s}{\Delta t}</math> | <math>v_{avg} = \frac{\Delta s}{\Delta t}</math> | ||
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where <math>\Delta s</math> is the distance traveled during the time interval <math>\Delta t</math>. | where <math>\Delta s</math> is the distance traveled during the time interval <math>\Delta t</math>. | ||
The difference lies in the fact that the magnitude of the displacement of a moving particle over a specific time interval may not equal the distance it traveled during that time interval. The displacement of the particle is merely the difference between its final and initial positions, and its magnitude is simply the straight line distance between those points. It does not depend on the path taken by the particle to get between those positions. The distance traveled, however, is the length of the path taken by the particle. The magnitude of the displacement of a moving particle over a specific time interval only equals the distance it traveled during that time interval if it traveled in a straight line for the duration of the interval. If there are any curves or turns, the distance traveled by the particle is greater than its displacement, so the particle's average speed is greater than the magnitude of its average velocity. | |||
[[File:Avgspeedvsavgvel.png]] | |||
Consider a particle moving at a constant speed along a curving path for some time period. It makes sense that the magnitude of its average velocity over that time period is lower than its constant speed because the particle's velocity at certain points in time partially or completely cancels with its velocity at other points in time. | |||
==Examples== | ==Examples== | ||
Revision as of 16:45, 6 August 2019
This is a short page aiming to differentiate between speed and velocity. For more detailed information on either of those topics, view their respective main pages.
The Main Idea
Speed ([math]\displaystyle{ v }[/math]) and velocity ([math]\displaystyle{ \vec{v} }[/math] or v) are similar concepts, and as a result, the terms are often confused and interchanged incorrectly in everyday conversation. The key difference between them is that velocity is a vector quantity that describes both how fast and in which direction an object is moving, while speed is a scalar quantity that describes only how fast an object is moving. Speed is the magnitude of the velocity vector. Velocity is the more descriptive of the two, as it contains all of the information speed contains and then some. It is easy to tell the speed of an object given only its velocity, but it is impossible to tell the velocity of an object given only its speed because one has no way of knowing the object's direction of travel.
Both speed and velocity have the same units because a vector always has the same units as its magnitude. Both are measured in units of distance over units of time. The SI unit for both speed and velocity is the meter per second (m/s). Both speed and velocity are instantaneous values and can change over time.
Mathematical Relationship Between Speed and Velocity
The following formulas describe the relationship between speed and velocity and can be helpful when converting between the two:
[math]\displaystyle{ v = |\vec{v}| }[/math]
[math]\displaystyle{ v = \sqrt{v_x^2 + v_y^2 + v_z^2} }[/math] (in 3 dimensions)
[math]\displaystyle{ \vec{v} = v\hat{v} }[/math], where [math]\displaystyle{ \hat{v} }[/math] is the direction of travel
Average Speed vs Average Velocity
One of the biggest sources of confusion between speed and velocity is the difference between average speed and average velocity. This is because although instantaneous speed is the magnitude of instantaneous velocity, average speed may not be the magnitude of average velocity. To understand why, let us take a look at the following formulas:
[math]\displaystyle{ \vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t} }[/math]
where [math]\displaystyle{ \Delta \vec{r} }[/math] is the displacement (change in position) over that time interval ([math]\displaystyle{ \Delta \vec{r} = \vec{r}_f - \vec{r}_i }[/math]).
[math]\displaystyle{ v_{avg} = \frac{\Delta s}{\Delta t} }[/math]
where [math]\displaystyle{ \Delta s }[/math] is the distance traveled during the time interval [math]\displaystyle{ \Delta t }[/math].
The difference lies in the fact that the magnitude of the displacement of a moving particle over a specific time interval may not equal the distance it traveled during that time interval. The displacement of the particle is merely the difference between its final and initial positions, and its magnitude is simply the straight line distance between those points. It does not depend on the path taken by the particle to get between those positions. The distance traveled, however, is the length of the path taken by the particle. The magnitude of the displacement of a moving particle over a specific time interval only equals the distance it traveled during that time interval if it traveled in a straight line for the duration of the interval. If there are any curves or turns, the distance traveled by the particle is greater than its displacement, so the particle's average speed is greater than the magnitude of its average velocity.
Consider a particle moving at a constant speed along a curving path for some time period. It makes sense that the magnitude of its average velocity over that time period is lower than its constant speed because the particle's velocity at certain points in time partially or completely cancels with its velocity at other points in time.
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