# How does average velocity differ from instantaneous velocity?

Jul 8, 2014

Instantaneous velocity is the velocity of an object at an instant in time. Average velocity is the mean velocity over a period of time.

Consider the tip of the second hand of a clock. It completes a full revolution of the clock face in one minute. In terms of the radius of the second hand, $R$, the instantaneous velocity is given by:

v=(2πr)/60

The reference point for measuring the instantaneous velocity is the location of the second hand. The direction of the velocity would be a tangent to the circle at that point. (The magnitude of the velocity will be constant at all points of the circle.)

The average velocity needs to be measured from a fixed reference point and it will change as the hand completes its revolution. If we use the zero seconds point as the reference point then the average velocity at various points will be:

• 15 second mark: $v = \frac{1.41 R}{15}$ (direction is 45º down and right)

• 30 second mark: $v = \frac{2 R}{30}$ (direction is vertically down)

• 45 second mark: $v = \frac{1.41 R}{15}$ (direction is 45º up and right - this is opposite to the 15 second mark)

• 60 second mark: $v = \frac{0}{60} = 0$