Average Velocity and Final Instantaneous Velocity

[Ibraheem]

Main Question or Discussion Point

Suppose a body moving in a curved path at a constant speed would its average velocity for a specific time period equal its final instantaneous velocity at the end of this period ?

 

[Orodruin]

No.

Consider a circular motion after one full rotation. The average velocity is zero (you returned to the original position!).

 

[DEvens]

To expand on what Orodruin said: Consider a mass moving in a circle at a constant speed. After one revolution it will have returned to the point it started. So its average velocity is zero. But its instantaneous velocity is clearly not zero.

 

[Ibraheem]

Thank you for replying
So if we consider a circular path, I suppose that the instantaneous velocity will equal the constant speed since the magnitude of the displacement vector will equal the distance at some instance during the period ?

 

[Nugatory]

Thank you for replying
So if we consider a circular path, I suppose that the instantaneous velocity will equal the constant speed since the magnitude of the displacement vector will equal the distance at some instance during the period ?

To be precise, the magnitude of the instantaneous velocity will equal the constant speed.
That's a bit of a tautology though, because speed is defined to be the magnitude of the velocity.

 

[sophiecentaur]

Thank you for replying
So if we consider a circular path, I suppose that the instantaneous velocity will equal the constant speed since the magnitude of the displacement vector will equal the distance at some instance during the period ?

If the path is curved then v_{(instantaneous)} is changing all the time. Its magnitude is constant (same value as its unvarying speed) and direction is what is changing.
"Average" Velocity (which should be called Mean Velocity because there are a number of other values of a varying quantity that can also be called 'Average') will be displacement in a given time divided by time. Counter intuitively, it can be anything from 'speed' in tangential direction to zero (instantaneously). But that's vectors for you.