Average Speed vs. Average velocity

[caprija]

Do you think that average speed and average velocities are usually the same for something in motion?

 

[radou]

Generally, they are synonyms, but velocity is usually used in the context of physics, I guess.

 

[caprija]

Generally, they are synonyms, but velocity is usually used in the context of physics, I guess.

Ya I mean in Physics.

Are they the same? what are the differences?

 

[radou]

I guess there's no difference, except that you usually don't use the term 'speed' in physics.

 

[caprija]

I guess there's no difference, except that you usually don't use the term 'speed' in physics.

Thanks

I have one more question, to find the instantaneous speed between let's say 0 and 3 seconds using a distance vs. time graph. I first draw the line fo best fit then I would find the slope right?

 

[MeJennifer]

Do you think that average speed and average velocities are usually the same for something in motion?

It is like comparing apples and pears, they are completely different. One is a scalar the other is a vector quantity.

 

[neutrino]

Actually, the average speed is the \frac{total distance travelled}{total time taken}, while average velocity is \frac{total displacement}{total time taken}. Remember, the displacement can be zero when the distance is not.

 

[caprija]

It is like comparing apples and pears, they are completely different. One is a scalar the other is a vector quantity.

ok so I'm confused now, when we're talking about something in MOTION is the average speed and the average velocity usually the same?

 

[radou]

Actually, the average speed is the \frac{total distance travelled}{total time taken}, while average velocity is \frac{total displacement}{total time taken}. Remember, the displacement can be zero when the distance is not.

Hm, could you clarify what you meant by that?

 

[Omega_6]

Hm, could you clarify what you meant by that?

It is possible to have an average velocity of zero, for example.

(You travel at 5 m/s for 2 sec and then you travel at -5 m/s (backwards) for 2 sec)

...and not so with speed (it is a scalar quantity).

 

[radou]

It is possible to have an average velocity of zero, for example.

(You travel at 5 m/s for 2 sec and then you travel at -5 m/s (backwards) for 2 sec)

I know, but I still don't understand the statement above. Nevermind.

 

[caprija]

I wrote:

"I do think that average speed and average velocity are usually the same for something in motion because it's still measuring time. The only diffference is that when calculating the velocity, you're calculating the rate at which the object changes it's postition."

does that sound about right?

 

[neutrino]

I know, but I still don't understand the statement above. Nevermind.

Went offline for some time...What exactly did you not understand?

 

[Checkfate]

Speed is a scalar quantity. If we designate forwards as positive movement and backwards as negative movement. I can run back and forth at 1m/s and arive where I started and my speed would still be 1m/s.

Now if we are using velocity, it is a VECTOR quantity. This means that you need to indicate MAGNITUDE and DIRECTION.

If you were to run 30,000 miles forward and then 30,000 miles backwards in 3 hours, your speed would be v=\frac{60000miles}{3hours}=\frac{20000miles}{hour}

BUT if you were to give velocity... \vec{v}=\frac{(30000miles)+(-30000miles)}{3hours}=\frac{0miles}{3hours}=\frac{0miles}{hr}

Get it?

Notice the arrow above v to designate whether it is a scalar quantity of a vector quantity.. \vec{v}=velocity v=speed

 

[radou]

...BUT if you were to give velocity... \vec{v}=\frac{(30000miles+(-30000miles)}{3hours}=\frac{0miles}{3hours}=\frac{0miles}{hr}

Get it?

Notice the arrow above v to designate whether it is a scalar quantity of a vector quantity.. \vec{v}=velocity v=speed

If you are so 'aware' of the difference between vector and scalar quantities, then you should be more careful when writing equalities.

 

[caprija]

Speed is a scalar quantity. If we designate forwards as positive movement and backwards as negative movement. I can run back and forth at 1m/s and arive where I started and my speed would still be 1m/s.

Now if we are using velocity, it is a VECTOR quantity. This means that you need to indicate MAGNITUDE and DIRECTION.

If you were to run 30,000 miles forward and then 30,000 miles backwards in 3 hours, your speed would be v=\frac{60000miles}{3hours}=\frac{20000miles}{hour}

BUT if you were to give velocity... \vec{v}=\frac{(30000miles)+(-30000miles)}{3hours}=\frac{0miles}{3hours}=\frac{0miles}{hr}

Get it?

Notice the arrow above v to designate whether it is a scalar quantity of a vector quantity.. \vec{v}=velocity v=speed

Yes, Thanks I get it.

But the question is really confusing, are they usually same or not?

 

[neutrino]

If you're moving with a constant velocity (speed is constant, direction is constant), then the magnitude of average velocity = average speed. In such a case, the dist-time graph will always be a straight line.

 

[Checkfate]

In every day conversation, if someone were to ask you what velocity your ride can get you to school and back, and you're school is 200m away from your home, they are confusing speed with velocity. Let's say your car can get to school and back home in 10 minutes, well the velocity is \vec{v}=\frac{200m+(-200m)}{10min}=0m/min This would be correct, but obviously they are asking for speed.

While in school, I would say that velocity and speed are NEVER the same past grade 10. If a question asks for the velocity, you must take vectors into account as giving the speed will be wrong! Speed is NOT velocity, even though many people whom forget about physics class assume it is :P Get it?

 

[Checkfate]

Even if you are traveling in a straight line in a forward direction at 10m/s, your velocity would be +10m/s while your speed is 10m/s... Small differance, but one indicates the direction, the other does not.

 

[caprija]

Even if you are traveling in a straight line in a forward direction at 10m/s, your velocity would be +10m/s while your speed is 10m/s... Small differance, but one indicates the direction, the other does not.

lol you thanks for trying.

I'm in grade 10, so this is all new to me. We're learning how to calculate average speed/velocity and instantaneous speed/velocity using secent and tangent methods.

 

[caprija]

I forget how to calculate the instantaneous velocity and speed using a graph.

 

[Checkfate]

Hehe, you do that through calculus :)

By "tangent methods" do you mean differentiation? Have you ever heard the term derivative? I am in grade 12 and am just learning about it now :P

But to calculate the ALMOST instantaneous speed using a graph, simply draw a secant from one point to a point fairly close and estimate the slope. I think that's about as close as you can get without using calculus.

Just remember these definitions, they are right out of my physics book.

vector : A quantity, such as velocity, completely specified by a magnitude and a direction.

scalar : A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction.

If you take physics 20 next year, you will learn plenty about vectors and scalars, :).

 

[caprija]

Hehe, you do that through calculus :)

By "tangent methods" do you mean differentiation? Have you ever heard the term derivative? I am in grade 12 and am just learning about it now :P

But to calculate the ALMOST instantaneous speed using a graph, simply draw a secant from one point to a point fairly close and estimate the slope. I think that's about as close as you can get without using calculus.

Just remember these definitions, they are right out of my physics book.

vector : A quantity, such as velocity, completely specified by a magnitude and a direction.

scalar : A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction.

If you take physics 20 next year, you will learn plenty about vectors and scalars, :).

Thanks for the definitions, I wrote them down lol

i got the instantaneous speed, how would calculate the instantaneous velocity? Which points do you use?

The question asks "What is the instantaneous velocity between 0 and 3 seconds?"

To get the speed I i used rise/run (line of best fit) got 2/3 = 0.7 km/min

which points do i use to find the instantaneous velocity?

 

[radou]

...
vector : A quantity, such as velocity, completely specified by a magnitude and a direction.
...

Whoa, slow down just a little bit. A vector is completely specified by: magnitude ; direction ; orientation.

http://csep10.phys.utk.edu/astr161/lect/history/velocity.html"

Case closed.

 

[Checkfate]

I have not yet seen a vector where the orientation was declared. But anyways.

 

[radou]

I have not yet seen a vector where the orientation was declared. But anyways.

What's the difference between \vec{v} and -\vec{v}?

 

[Checkfate]

2v :P

caprija, about your question :) "What is the instantaneous velocity between 0 and 3 seconds?"

It sounds like the question is asking you for the average velocity between 0-3s. So your approach is right, you would take two points that lie on the on the line of best fit between x=0 and x=3 and then calculate the slope of that line. :) If you want to show your teacher that you understand it is a velocity (vector) then put \vec{v}=+0.7km/min :)

Is the portion of the graph between 0-3s a straight line?

 

[radou]

...If you want to show your teacher that you understand it is a velocity (vector) then put \vec{v}=+0.7km/min :)

This would definitely be a way of showing your teacher that you don't understand anything. Since when do vector quantities equal scalar quantities? You can talk about the magnitude of the velocity vector, but then you have to write \left|\vec{v}\right|=0.7 km/min.

 

[jtbell]

vector : A quantity, such as velocity, completely specified by a magnitude and a direction.
...

Whoa, slow down just a little bit. A vector is completely specified by: magnitude ; direction ; orientation.

http://csep10.phys.utk.edu/astr161/lect/history/velocity.html"

Case closed.

"Direction" and "orientation" mean the same thing in this context. The page that you refer to says:

It is also common to indicate a vector by drawing an arrow whose length is proportional to the magnitude of the vector, and whose direction specifies the orientation of the vector.

(I added the boldface for emphasis.)

 

[Checkfate]

Radou, I suppose you are correct on that one. To find the velocity you would need a displacement vs time graph, not a distance vs time graph. You do not have enough information on the graph to calculate velocity. My bad.

The reason, caprija, is because you are provided with a graph with the speed of the object, but not the direction, so it is not possible to come up with a velocity unless you use the method that radou mentioned. Sorry, I misunderstood for a second there.

 

[Checkfate]

If you are so 'aware' of the difference between vector and scalar quantities, then you should be more careful when writing equalities.

By the way, wth is this? Can you point out my error rather than just saying there is a mistake and I am not aware of the difference between scalar and vector quantities? Thanks.

 

[caprija]

2v :P

caprija, about your question :) "What is the instantaneous velocity between 0 and 3 seconds?"

It sounds like the question is asking you for the average velocity between 0-3s. So your approach is right, you would take two points that lie on the on the line of best fit between x=0 and x=3 and then calculate the slope of that line. :) If you want to show your teacher that you understand it is a velocity (vector) then put \vec{v}=+0.7km/min :)

Is the portion of the graph between 0-3s a straight line?

Thank you so muchhhhhhhh :)

You helped a lot :)

Thanks :)

 

[radou]

By the way, wth is this? Can you point out my error rather than just saying there is a mistake and I am not aware of the difference between scalar and vector quantities? Thanks.

Cool down, no one is insulting you. I just wanted to point out that you can't write (which you did in one of your previous posts, and if it was a mistype, then I apologize) something like \vec{v} = 0.7 [units] because it does not make any sense. However, you can write, for example, \vec{v}=0.7\vec{i} [units].

 

[Checkfate]

caprija, wait.. I was wrong. Since your graph is a distance vs time graph it is impossible to find velocity, read one page back. Sorry mate, I was in a rush and didn't really think it through. According to the data you have supplied, it is impossible to find the velocity. What course is this for? If you have not learned about vectors, maybe they just misused the word velocity and meant speed. To be safe I would put v=0.7m/min.
Unless you have a displacement time graph, then you could find velocity. :) But at least now you know the difference between velocity and speed, tell your teacher tommorow that you aren't able to find velocity because you don't know the displacement :P (displacement is the distance and direction by the way, whereas distance does not specify direction, you will learn about it soon.)

 

[Checkfate]

Radou, okay sorry, I did feel insulted as it felt like you were saying that I did not know what I was talking about while I feel strongly that I know the difference between a vector/scalar quantity. But eplain to me why you need the vector symbol on the units? In my physics class \vec{v}=0.7m/min would meen 0.7m/min in a positive direction (The + is assumed). We don't put a vector sumbol over 0.7m/min. If I am doing something wrong within this paragraph please tell me :) I can't say that I am failing physics though... and I think I would be if I didn't have a grasp on how to use vector quantities by this point! lol :) Why do you have \vec{i} in there?

 

[radou]

"Direction" and "orientation" mean the same thing in this context.

Hm, in my language, by mentioning 'direction', we refer to the straight line on which the vector is 'placed'. My fault, direct translation. But, how do you call that 'direction' then? (Assuming we know what magnitude means, and assuming when you say, for example, 'direction north', you mean that the 'arrow' is pointed north.)

 

[radou]

...In my physics class \vec{v}=0.7m/min would meen 0.7m/min in a positive direction (The + is assumed). We don't put a vector sumbol over 0.7m/min. If I am doing something wrong within this paragraph please tell me :) I can't say that I am failing physics though... and I think I would be if I didn't have a grasp on how to use vector quantities by this point! lol :) Why do you have \vec{i} in there?

Have you learned about vectors in math yet?

 

[Checkfate]

No, just physics. I have wanted to peak at vector calculus for a while now, but haven't yet.

 

[radou]

No, just physics. I have wanted to peak at vector calculus for a while now, but haven't yet.

I suggest you do so, it will become more clear.

 

[jtbell]

Hm, in my language, by mentioning 'direction', we refer to the straight line on which the vector is 'placed'. My fault, direct translation. But, how do you call that 'direction' then? (Assuming we know what magnitude means, and assuming when you say, for example, 'direction north', you mean that the 'arrow' is pointed north.)

I see your point. We can say that a line's orientation is horizontal, and its direction is either to the left or to the right. I think in practice, in English, "direction" almost always includes both things. People often do use "orientation" to mean what you do, but it's also used as a synonym for "direction" so it can be confusing unless the context is clear. I can't think of a word that people would reliably recognize as meaning your "direction," without a very clear context to put it in.

And with vectors specifically, the description "magnitude and direction" is universal in physics textbooks in the U.S., as far as I know.

 

[Checkfate]

radou I am sorry to say this but I think you are misinterpreting my point... We are dealing with a physics problem, and in physics, \vec{v}=0.7m/s is the correct way of writing that the velocity of something is 0.7m/s in a positive direction. I would beg to differ that I need to read a vector calculus book (university material) to understand vector notation which is clearly and simply laid out in grade 10 physics courses. While in vector calculus, one set of rules may be used, but as far as I know they don' teach vector calculus in grade 10 so I don't think that someone should have to understand a university level concept to grasp a grade 10 level concept...caprija's is in grade 10 after all. If you want to carry out this discussion further, perhaps we should move it to private discussion. I am not saying that you are not right as you obviously have a few years on me :P But in a physics courses in the United States and Canada, my definitions as well as my examples hold true. (except the one that I admitted was miscalculated) "Case Closed"

 

[radou]

I see your point. We can say that a line's orientation is horizontal, and its direction is either to the left or to the right. I think in practice, in English, "direction" almost always includes both things. People often do use "orientation" to mean what you do, but it's also used as a synonym for "direction" so it can be confusing unless the context is clear. I can't think of a word that people would reliably recognize as meaning your "direction," without a very clear context to put it in.

And with vectors specifically, the description "magnitude and direction" is universal in physics textbooks in the U.S., as far as I know.

I think I got it. A vector is completely described with magnitude and direction if we set up a coordinate system, because a point with the coordinate (x, y, z) is enough to determine the radius-vector from the origin, with the 'arrow' on the top, i.e. in the point (x, y, z). Further on, for every point (x, y, z), we can define the vector of an 'opposite orientation' with it's 'top' at the point (-x, -y, -z). Pointing out that the vector is described with three parameters, obviously makes sense only if we haven't got a coordinate system set up.