# B What's the difference between velocity and average velocity

1. Sep 24, 2016

### edephysic

Hello everyone,

The velocity and average velocity it is the same?
The formula of the velocity is: distance / time or [L] / [T]. The average velocity is it equal?

thanks

2. Sep 24, 2016

### Simon Bridge

"average velocity" is a kind of velocity but not all velocities are average velocities.
The average velocity is related to the velocity at a particular time the same way that an average score for a season is related to the score for an individual game.

When you travel in a car you will notice that the speedo does not read the same speed the whole time, nor does it steadily increase or decrease but more sort of wanders around ... also you change direction a number of times as you go.

The speed on the speedo and the direction of travel is what we usually referred to as "velocity". If we need to make a distinction then this is the instantaneous velocity. It tells you the rate that your position changes with time at that moment.

After that journey, your odometer will tell you how far you drove, and the clock will tell you how long it took to ravel that distance.
The average speed for the journey could be what that distance divided by that time. (which is usually the one you use.)

I said "speed" in that example for a reason: you got the formula wrong. Sure, velocity has dimensions of length over time but all velocities are vectors ... they have direction as well as size. That's why I talked about how the direction the car travelled was changing on the journey.

The average velocity is a vector - and it is the net displacement divided by the time ... the displacement is a vector that points from your start point to the end point of your journey, and it's length is the distance between the endpoints as the crow flies.

See the difference?

3. Sep 24, 2016

Staff Emeritus
My last trip had an average velocity of 30 miles per hour. What was my velocity when I was stopped at a light? See the difference?

4. Sep 24, 2016

### sophiecentaur

Actually, Velocity is defined as Displacement / time. The term Displacement tells you where you actually end up, rather than how many metres you wandered about on the way from A to B (which would tell you your Speed).
The above formula actually gives you the Average Velocity over the whole time of the experiment.
Velocity is a more sophisticated quantity because it refers to the instantaneous value. Calculus rears it ugly head here because the instantaneous velocity is what you get in the limit if you measure displacement/time for progressively smaller intervals of time (tending to zero). That would seem daft as it would be 0 divided by 0 but it actually works if you take the limit 'properly'. Let the Mathematicians worry about that sort of thing - it's OK because they say it is.

5. Sep 24, 2016

### robphy

The velocity depends on your motion now (hence the usually omitted "instantaneous").
As mentioned above, this depends on your speedometer reading and the direction of your motion now. (Implicitly, you have to specify when now is.) Physically, it depends on how your position is changing during the next teeny-tiny instant of time (without caring where you have been).

In principle, the average velocity depends on all of your generally-varying velocities and how much time you spent doing each, beginning from when you started up until when you end. (You have to specify the start and the finish.) You then compute the time-weighted average. It turns out that this is equal to the total displacement divided by the total elapsed time, unfortunately often quoted as the definition without explaining where the "average" comes from. Physically, it can be interpreted this way: the constant velocity needed to make the direct trip from starting position to ending position in the same elapsed time. (It's like the velocity of the Tortoise in the Tortoise and the Hare race that ends in a tie.)

If the velocity is constant throughout the trip, then the average velocity for the trip is equal to the velocity at each instant of the trip.

(Don't confuse velocity, speed, average, velocity, and average speed. They are generally different.)