# How to Calculate Average Velocity and Speed?

• Immy2000
In summary, a student traveled north and south at different speeds for a total of 40 minutes. The average speed was 6.9 m/s north and 6.875 m/s south.
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...

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

Last edited by a moderator:
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.

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"?

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

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

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.

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.

## What is the difference between velocity and speed?

Velocity is a vector quantity that refers to the rate of change of an object's displacement in a specific direction. Speed, on the other hand, is a scalar quantity that refers to the rate of change of an object's distance traveled. In other words, velocity takes direction into account while speed does not.

## How are velocity and speed related?

Velocity and speed are related in that they both involve the rate of change of an object's position. However, velocity includes direction while speed does not. In some cases, an object's velocity and speed may be the same if the object is moving in a straight line with a constant speed.

## What is the formula for calculating velocity?

The formula for velocity is v = d/t, where v is velocity, d is displacement, and t is time. This formula can also be written as v = Δx/Δt, where Δx is the change in position and Δt is the change in time.

## How do you calculate average speed?

Average speed is calculated by dividing the total distance traveled by an object by the total time taken. The formula for average speed is s = d/t, where s is average speed, d is distance, and t is time.

## What is the difference between instantaneous velocity and average velocity?

Instantaneous velocity refers to the velocity of an object at a specific instant in time, while average velocity refers to the average velocity of an object over a certain period of time. Instantaneous velocity can be found by taking the derivative of an object's position-time graph, while average velocity can be found by taking the slope of a line connecting two points on an object's position-time graph.

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