How to Calculate Average Velocity and Speed?

[Immy2000]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~Solved~~~~~~~~~~~~~

Homework Statement

A student travels at a constant velocity of 8.0 m/s north for 25 minutes, and then 5.0 m/s south for 15 minutes. Calculate the students...
(Answer in brackets)

a) Average Velocity (Answer 3.1 m/s North)
b) Average Speed (Answer 6.9 m/s)

Homework Equations

a) http://library.thinkquest.org/C0110840/Images/vel.gif

b) Vav = [Delta]d/[Delta]t

The Attempt at a Solution

a) Vav = [Delta]d/[Delta]t
[Delta]d = d2-d1
[Delta]t = t2-t1

t1= 0s
t2= 15 minutes = 900s

d1= 0m
d2= (5 m/s * 900s)

[Delta]d= 4500m - 0m = 4500m
[Delta]t= 900s - 0s

Vav = 4500 m
900 s
= 5.0 m/s [North]

? I do not even understand velocity, so I just plugged in what I thought seemed logical as initial start I assumed was 0 and if you travel from 0 to x1 and then from x1 to x2, it would therefore be x2 being the final..thing and 0 being the initial..thing.

b) Vav = [delta]d\[Delta]t
[Delta]t = [t2 + t1]
[Delta]d = [d2*t2] + [d1*t2]
[Delta]d = (8 m/s * 1500 s) + (5 m/s * 900 s) = 16500 m
[Delta]t = (900 s + 1500 s)
Vav = 16500 m
2400 s
Vav = 6.875 = 6.9 m/s

? WOW I don't even know why it worked because I always though it was d2-d1 not d1+d2. I am so confused! Please, all help would be much appreciated. :)
I just can't seem to understand velocity which probably is the cause of my inability to differentiate what to do for either speed or velocity in general..

Homework Statement

 

[nothing19]

Well for 1...
you want to take the distant traveled north. That's straightforward, just don't get stuck on units.
Remember, Distance = Speed * Time
Then measure the distanced traveled south, subtract that to have the total distance traveled.
You now will have a distance, and you know the time it took (25+15=40 min). D/T=V...so divide the distance by the time (convert back to seconds), and you'll get the right answer.

As far as average speed, that's even easier. You could just add the distance traveled in the first 25 to the distance in the other 15, and then divide that total distance by 40. Remember, speed doesn't take direction into account, just magnitude. Velocity is a vector and takes both magnitude and direction into account.

Hope that helps.

 

[Immy2000]

Alright, I understand speed now, but if I read correctly, you firstly address velocity. Isn't velocity "change in displacement", not "change in distance" over "change in time"?

 

[nothing19]

Yes, my bad. Should've said displacement, but the calculations are in fact calculating the displacement, not the distance.

 

[Immy2000]

When I did the calculation I got 6.9 m/s which is not the answer to average velocity, but rather average speed.

 

[nothing19]

Ah. you added the distances traveled. Remember when dealing with velocities you're dealing with vectors, and the vectors are in completely opposite directions here--the two must be subtracted.

 

[Immy2000]

OH MY GOSH I LOVE YOU THANK YOU SO MUCH! Heh. No really, thanks, that really helped. Its so simple...I guess I just need to break it down and go from there. For now.