A particle moves with constant speed v along a regular hexagonal A B C D E F in same order (i.e., A to B, B to C, C to D, D to E, E to F and F to A). The magnitude of average velocity for its motion from A to C is

See figure. The average velocity is given by Average velocity = total displacement  total time âˆ´vav=ACt or vav=ACtThe time taken by the particle to reach from A to C ist=AB+BCV=2aV....(1)From â–³ABC we havecos⁡120∘=a2+a2−(AC)22a2or  - 12=2a22a2−(AC)22a2Solving we get, AC=3a...(2)Now vav=3a2a/v=3v2