Average speed and average velocity?

[Owais Iftikhar]

Average speed and average velocity??

Hello
Dose a particle having a uniform circular motion may have some average velocity, although it is accelerating?? And how to find it? If yes, it has some average velocity then, what's its relation with average speed?
"IAM CONFUSED THAT THE PARTICAL VELOCITY IS KEEP ON CHANGING DUE TO CHANGE IN IT'S VECTOR'S DIRECTION SO CAN WE APPLY SIMPLE STRIGHT LINE MOTION FORMULA (CHANGE IN VELOCITY/CHANGE IN TIME) OR SOME SPECIAL FORMULA??"

 

[Fermat]

Average speed is simply the distance covered divided by the time taken to cover that distance.

Average velocity is a bit different, since velocity is a vector.

When working with vectors, then the average velocity is the simple average of the initial and final velocities.
For example, in circular motion. Let the initial velocity at some point be v.
After half a revolution, or 180 degrees, the velocity will be -v.
So, in the case of movement around half a circle, the average velocity is $$(v_f + v_i)/2 = (\mathbf{v} - \mathbf{v})/2 = 0$$
When a full circle is traversed, the final velocity will be v again, the same as the starting velocity, and in this case, the average velocity will be $$(v_f + v_i)/2 = (\mathbf{v} + \mathbf{v})/2 = \mathbf{v}.$$
So, in circular motion, although the average speed is constant, the average velocity depends on the distance traversed.