# Average speed vs. Average velocity

#### shahar

##### Full Member
What is the difference between these two?

#### Subhotosh Khan

##### Super Moderator
Staff member
What is the difference between these two?

Tell us what you find - and what are you confused regarding the responses you found.

#### shahar

##### Full Member
O.K. I will ask it differently:
When they are equal?
and when they are have not the some values?
In a system of the two same bodies?

#### Subhotosh Khan

##### Super Moderator
Staff member
O.K. I will ask it differently:
When they are equal?
and when they are have not the some values?
In a system of the two same bodies?
OK,

Do a Google search and tell us what you found!

Tell us exactly where you are confused!

#### Dr.Peterson

##### Elite Member
O.K. I will ask it differently:
When they are equal?
and when they are have not the some values?
In a system of the two same bodies?
Why would two bodies be involved, in a question about one average speed or velocity? If there is more background for your question, tell us! How many dimensions do you have in mind?

Do you know the difference between speed and velocity, ignoring "average"?

#### HallsofIvy

##### Elite Member
"Speed" is a number, "velocity" is a vector function. It includes both speed and direction.

If my velocity is "50 mph southeast" my speed is "50 mph".

If I go 10 miles east at 30 mph and then 10 miles west at 30 mph I wind up right back where I started as if I hadn't moved at all. My average speed was 30 mph but my average velocity was 0 mph,

#### skeeter

##### Elite Member
average velocity $$\displaystyle = \frac{\int_{t_0}^{t_f} v(t) \, dt}{t_f - t_0}$$

average speed $$\displaystyle = \frac{\int_{t_0}^{t_f} |v(t)| \, dt}{t_f - t_0}$$

#### Dr.Peterson

##### Elite Member
You may observe that the last two answers relate to different interpretations of the question: HallsofIvy assuming two dimensions, skeeter assuming one dimension. In essence, they mean the same thing, but that takes different forms: a sum/integral of vectors/signed numbers (velocities), vs. a sum/integral of absolute values (speeds). This is why I asked about dimensions, and other clarifications to the context of your question.

#### Subhotosh Khan

##### Super Moderator
Staff member
average velocity $$\displaystyle = \frac{\int_{t_0}^{t_f} v(t) \, dt}{t_f - t_0}$$

average speed $$\displaystyle = \frac{\int_{t_0}^{t_f} |v(t)| \, dt}{t_f - t_0}$$
In mechanics, the definition is:

average constant speed of a particle = (distance travelled by the particle in time δt)/(δt) ........................................ distance is a scalar quantity

average constant velocity of a particle = (displacement the particle in time δt)/(δt) ........................................ displacement is a vector quantity

Instantaneous speed is the magnitude of the instantaneous velocity.​
Average constant speed is NOT the magnitude of the average constant velocity.​

The integration mentioned above (for v(t)) would be line integration or contour integration (of the vector) along the path. Complication arises in a curved path - more non-intuitively in a self-intersecting path.

#### skeeter

##### Elite Member
In mechanics, the definition is:

average constant speed of a particle = (distance travelled by the particle in time δt)/(δt) ........................................ distance is a scalar quantity

average constant velocity of a particle = (displacement the particle in time δt)/(δt) ........................................ displacement is a vector quantity

Instantaneous speed is the magnitude of the instantaneous velocity.​
Average constant speed is NOT the magnitude of the average constant velocity.​

The integration mentioned above (for v(t)) would be line integration or contour integration (of the vector) along the path. Complication arises in a curved path - more non-intuitively in a self-intersecting path.