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.

 

[quicknote]

Hello,

Average speed and average velocity are two different measures of motion. Average speed is the total distance traveled divided by the total time taken. This means it is a scalar quantity and does not take into account the direction of motion. On the other hand, average velocity is the displacement divided by the total time taken. This means it is a vector quantity and takes into account the direction of motion.

In the case of a particle undergoing uniform circular motion, it is constantly changing direction and therefore, the velocity is constantly changing. However, we can still calculate the average velocity by taking the total displacement (which is zero) and dividing it by the total time taken. This will give us the average velocity, which will also be zero in this case.

The formula for average velocity is the same as the formula for average speed, which is change in position divided by change in time. However, in the case of average velocity, we need to consider the direction of motion and use vector quantities for displacement and time.

I hope this clears up your confusion. It is important to understand the difference between average speed and average velocity in order to accurately describe and analyze motion.