Question

Explain clearly, with examples,the distinction between: 

Magnitude of average velocity over an interval of time, and the average speed over the same interval [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval] Show in both (a) and (b) that the second quantity is either greater than or equal to the first.when is the equality sign true?

Answer 1

Magnitude of average velocity

= magnitude of displacement/time interval = AC/t

and Average speed = total path length/time interval = (AB + BC)/t

As, (AB + BC) > AC, so average speed is greater than the magnitude of average velocity. If the particle is moving along a straight line, then in a given time the magnitude of displacement is equal to total path length traversed by particle in that time, so average speed is equal to magnitude of average velocity.