Difference between average speed, instantaneous speed, velocity, acceleration? help!

[bjr_jyd15]

Hi I'm in an honors physics class. I don't really understand the difference between average speed and instantaneous speed. Say I'm given in data table with time (s) and distance (m). How can I find each of these? Is there a formula?

Also, what is the relationship of velocity with acceleration? My teacher said constant velocity means no acceleration? I'm not sure that makes sense?!

One more thing: What is the difference between displacement vectors and resultant vectors? I seem to be stuck. I know for one you just add the magnitudes but for the other it's pythagorean.

Any help would be great!

[Ba]

Average velocity is the velocity between two points in time the slope of a line between those two points), instantaneous velocity is the speed at one point (this is found by calculus and the derivitive usually, it's the slope at that point).
Acceleration is the change in velocity over time therefore for an unchanging velocity you get nothing divided by time so acceleration is nothing.

[Tide]

Average speed is the total distance traversed divided by the total time required to get there.

Instantaneous speed is the speed at an instant in time and can be viewed as the distance traversed divided by the traversal time as the traversal time is made arbitrarily small. It can be written as a derivative.

In particular, velocity is a vector quantity
\vec v = \frac {d \vec x}{dt}
where \vec x is the (vector) displacement.

A displacement vector is a vector describing the difference in location from one point to another. A resultant vector is a vector that results from adding or subtracting vectors. A resultant vector can also be a displacement vector.

[robphy]

Average velocity is the velocity between two points in time the slope of a line between those two points), instantaneous velocity is the speed at one point (this is found by calculus and the derivitive usually, it's the slope at that point).
Acceleration is the change in velocity over time therefore for an unchanging velocity you get nothing divided by time so acceleration is nothing.

For consistency with your discussion of average-velocity and instantaneous-velocity, you should really say "average-Acceleration is the change in velocity over time". Instantaneous-acceleration is the acceleration at one point (found by calculus using the derivative...it's the slope at that point [on a velocity-vs-time graph])".

[bjr_jyd15]

So when finding change in distance I should use displacement vectors right? If so , then when are resultant vectors ever useful?

Thanks.

[recon]

I'm not sure how to phrase it, but resultant vectors can also be used to find out the net velocity of an object if it is being influenced by more than two different velocities.