A particle goes from point A to point B in 1.0 seconds moving in a semicircle of radius 1.0. What is the magnitude of the average velocity?
By, definition, the average velocity on the time interval `Delta t ` is the displacement vector divided by this time interval:
`vec v_(avg) = (Delta vecr)/(Delta t) = (vecr_f - vec r_i)/(Deltat)`
Note that average velocity and the displacement are vector quantities. The displacement is the vector difference between the final and initial position vectors.
As the particles moves from point A to point B in a semicircle, the displacement of the particle is a diameter of the semicircle (please see the attached image for illustration.)
The magnitude of the average velocity is then the length of the diameter of the semicircle divided by the time interval:
`|vec v_(avg)| = (|Delta vecr|)/(Deltat)` , `|Delta vecr| = d` , the length of the diameter of the semicircle. Since the radius of the semicircle is 1, the diameter is double the radius, or 2.
The magnitude of the average velocity is
`|vec v_(avg)| = 2/1 = 2` (units per second, the units in which the radius is measured is not given here.)
The magnitude of the average velocity is 2.