Average Velocity Question: Solving for Average Velocity in Complicated Motion

[mcolem]

I'm having trouble solving part of this problem. Can anyone help?

In climbing a wall, a caterpillar undergoes a complicated motion in which it ascends 3m and slips down 2m every 5min. What is its average speed and average velocity after 5min?

I figured the avg. speed to be 0.02 m/s, but I'm having trouble with the avg. velocity. It's not making sense to me. The displacement is needed to find the solution, but I'm having a hard time determining the intial and final positions.

 

[Mattara]

speed and velocity is the same...

:S

 

[Mindscrape]

speed and velocity is the same...

:S

Err, no. Where did you get that from?

Well, it only asks you for the velocity after 5 minutes so there won't be any sort of fractional constants we have to use, which makes it nice since it gives the motion of the catapiller in a 5 minute time frame. I'll isolate the pieces you want to look at, and see if you can't get it.

ascends 3m and slips down 2m
after 5min

What is the definition of displacement? What is the definition of velocity?

Also, even though .02 m/s would be right, you should use 3 significant figures so it is .0166m/s.

 

[HallsofIvy]

Speed is the magnitude of the velocity vector. In this case, since the motion is in a straight line and positive, yes, speed is the same as velocity!

 

[robphy]

"ascends 3m" is "positive"
but "slips down 2m" is not...

 

[PPonte]

I think it's not difficult to determine the final and initial positions since the caterpillar ascends 3m and slips down 2m every 300 s.

 

[Mattara]

Err, no. Where did you get that from?

I refer to HallsofIvy

you should use 3 significant figures so it is .0166m/s.

...It is often bad pratice to use more significant numbers in the answer that there is in the question. There were one sign. fig. in the figure and therefore the answer would be 0.02.

"ascends 3m" is "positive"
but "slips down 2m" is not...

yes, but the motion after the stated 5 min is positive and that is what i meant. Sorry for the confusion.

 

[robphy]

"ascends 3m" is "positive"
but "slips down 2m" is not...

yes, but the motion after the stated 5 min is positive and that is what i meant. Sorry for the confusion.

What your statement implies is that both the average speed and the average velocity will be positive... but not that they are equal. If the motion is always (that is, for every value of t [treated continuously..not merely intervals]) positive, then average speed can be numerically equal to the average velocity.

The following may helpful:

average velocity depends on displacements (final minus initial position)
average speed depends on distance-travelled (which could be measured by the wear due to friction on your automobile tires [since friction doesn't care if you travel forward or backward])
[These statements can be justified by writing the [real] definitions of average velocity and average speed.]

In this problem, is the [magnitude of the] total displacement equal to the distance travelled?