# Homework Help: Average speed relative to the magnitude of the average velocity?

1. Jun 24, 2010

### rws_killer5

What can be said about average speed relative to the magnitude of the average velocity?
a) greater than
B) equal to
C)both a and B

I think it is neither because average velocity is displacement/total time and average speed is distance/total time.

Since displacement is always equal to or less than distance, average velocity is always equal to or less tahn average speed.

Also, when it says magnitude, does it mean it is a positive number?

2. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

What is different about speed versus velocity. There is a fundamental difference, which I think you will need to address in order to answer this question.

3. Jun 24, 2010

### rws_killer5

Re: Velocity/Speed?

umm what??!?

4. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

What you didn't understand my question, or what you don't know the answer and are asking what the answer is?

5. Jun 24, 2010

### rws_killer5

Re: Velocity/Speed?

6. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

Hint: which is a vector?

7. Jun 24, 2010

### rws_killer5

Re: Velocity/Speed?

an arrow that represents magnitude and direction

8. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

Well, that's one way to describe a vector, yes. But I asked which of speed and velocity is a vector. Why did I ask that, and what is the answer?

9. Jun 24, 2010

### rws_killer5

Re: Velocity/Speed?

velocity. When it says magnitude of vector, that means it needs to be positive right?

Btw, I am learning physics by myself. So even if you give me more information than necessary, don't worry, you are not committing any academic integrity issues.

10. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

Correct. Velocity is a vector, with magnitude and direction. Speed is just the absolute value, and is always positive.

So if you drive your car to the market and back at a constant speed S, what is the average speed? If you show the vector velocity for that same trip, what is different about velocity for the two legs of the trip? Does that help lead you to the answer for the original problem?

11. Jun 24, 2010

### rws_killer5

Re: Velocity/Speed?

i'm sorry, but you are doing a really bad job at answer the questions that I ask. once again, when it says "magnitude" does magnitude mean it is always positive?

Velocity shows magnitude and direction. The question states the magnitude of velocity. Therefore velocity cannot show direction and is therefore always positive value correct?

12. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

Well, I think you will need to look in your book to see how it handles the definition of vectors. If it says the magnitude is always positive, then that's pretty much the same as speed.

13. Jun 24, 2010

### Staff: Mentor

Re: Velocity/Speed?

So far, so good. (Those are the standard definitions, but some books can vary. Check your book.)

Makes sense to me.

So which answer makes most sense? What's your opinion about each of the choices? (The question could have been phrased better. Are you sure you've copied it exactly as it was given?)

Yes, magnitude is always positive.

14. Jun 24, 2010

### sona1177

Re: Velocity/Speed?

Yes, magnitude can not be negative. Speed is a scalar, not a vector. By definition speed is the magnitude of the velocity. This should help. Therefore they must be equal.

15. Jun 25, 2010

### ehild

Re: Velocity/Speed?

Right, but the average speed need not be the same as the magnitude of average velocity.

ehild

16. Jun 25, 2010

### sona1177

Re: Velocity/Speed?

But neither is not a choice. In this case if you assume that by average speed he means something like the speed is the same going and returning then the average speed will be equal to the velocity, right? I just started a Physics course (you helped me with a Kinematics question) so if I am wrong, please correct me? Thank You!

17. Jun 25, 2010

### ehild

Re: Velocity/Speed?

The average speed can be either equal or higher than the magnitude of the average velocity.
If a body moves from point A to B, d distance away, along a straight line in time t, the average speed is the distance between A and B divided by the time: d/t. The average velocity is the displacement from A to B divided by the time, a vector quantity, whose magnitude is positive it is d/t again.

If the body moves from A to B and returns back, its average speed is the length of its path, 2d, divided by the time.

The average velocity is the total displacement which is zero now, divided by the time, so the magnitude of the average velocity is zero now.

In general,the average speed is the length of the path taken, divided by the time, and the average velocity is the displacement divided by time. The displacement is a vector connecting the starting point of the trajectory to the end point. The magnitude of the displacement is the length of the straight line connecting those points, which is never longer than any curve connecting the same points.

ehild

18. Jun 25, 2010

### sona1177

Re: Velocity/Speed?

sona1177 Says: 06:53 AM

Quote ehild
Right, but the average speed need not be the same as the magnitude of average velocity.

ehild
But neither is not a choice. In this case if you assume that by average speed he means something like the speed is the same going and returning then the average speed will be equal to the velocity, right? I just started a Physics course (you helped me with a Kinematics question) so if I am wrong, please correct me? Thank You!

19. Jun 25, 2010

### sona1177

Re: Velocity/Speed?

Thank you so much for that clarification! Basic things like this sometimes mess me up in a problem so I'll keep it in mind.

20. Jun 25, 2010

### rws_killer5

Re: Velocity/Speed?

btw i was sick yesterday so i wasn't thinking clearly. I basically answered the question in my first response. The answer is C.

I basically said that avg velocity is always less than or equal to avg speed. So avg speed is always equal to or greater than avg velocity. My bad guys...