# Why is average velocity called velocity?

1. Apr 18, 2015

### NooDota

1. Excuse the dumb questions, I've just started learning physics outside my school course. If this forum doesn't allow this level of questions, then please point me somewhere else.

2. I'm also not sure if I'm allowed to post multiple questions that fall under the same topic, I didn't see anything in the guide lines about that.

3. This is my first post, please tell me if I did something wrong.

1. The problem statement, all variables and given/known data

First, why is average velocity called like that? From my understanding, it refers to the amount of displacement in the given time period, so if you go from point A and back to A, your average velocity is 0, but that doesn't exactly refer to velocity. Am I right?

2. When is Vavg useful to me? When do I use it? Can someone give me examples please?

2. Relevant equations

3. The attempt at a solution

Also, on a side note (I'm not sure if side notes are allowed), I've started reading the book "Fundamentals of Physics by David Halliday", my main language isn't English, so it's a bit hard to get used to all the scientific terms. It's my first physics book (outside my school course) that I've decided to learn, does anyone recommend any other books, or is this one appropriate? Thank you.

2. Apr 18, 2015

### brainpushups

Correct. Average velocity is the total displacement divided by the time interval of the displacement. In fact, any average rate is the total change in the particular quantity over the total time. Average velocity is different from instantaneous velocity. If you are just getting used to these terms it is probably helpful to think of instantaneous velocity to be the ratio of displacement to a very very very short time interval.

Because instantaneous velocity is a vector it includes information about the direction of travel which is useful information. If the total displacement over the entire time is zero then the average velocity will indeed be zero. If you want to know something about average the way in which the object was moving it might be useful to calculate the average speed which is the total distance traveled divided by the time interval instead.

I would say that instantaneous velocity is no doubt the more useful quantity, but average values of any quantity can be useful sometimes. Here is an example: suppose you drop an object from rest and it falls for 2 seconds. The change in velocity (down measured as positive for convenience) is about 20 m/s. How far did the object fall? Well, if you know the kinematic equations this can be answered easily, but it can also be answered easily using the average velocity. The average velocity over the time interval is 10m/s and it fell for 2 seconds so the displacement is

Δx = vave*Δt = 20m

Another place where this is often used is with the average force and the change in momentum.

3. Apr 18, 2015

### AlephNumbers

Me too, I think it's a good book. You might want to learn some basic differential and integral calculus in order to get the most out of it. You will mostly only need to differentiate or integrate polynomials, so I would advise at least learning the generalized power rule.

4. Apr 18, 2015

### Staff: Mentor

Right.
Where is the problem? You are at the same point again, in total you did not change your position. You get the same result if you move with the average velocity of zero for the same time period.

It is useful if you are not interested in details of the motion, but just in the result.

For example, let's say you want to go from town A to B, distance 80 kilometers, in one hour. To get there, you need an average velocity of 80 km/h. It does not matter if you drive 80km/h for one hour, or 100 km/h for 30 minutes and 60 km/h for 30 minutes.