A particle moves with constant speed `v` along a regular hexagon `ABCDEF` in the same order. Then the magnitude of the avergae velocity for its motion form `A` to

Options

A. `v`
B. `v/2`
C. `(sqrt(3)v)/2`
D. none of these

Explanation

(c) Average velocity `=("Total displacement")/("Total time")`
`v_(av)=(AC)/t :. |v_(av)|=(AC)/t`

The time taken by particle to reach from `A` to `C` is
`t=(AB+BC)/v=(2a)/v`
In`DeltaABC, cos 120^(@)=(a^(2)+a^(2)-AC^(2))/(2a^(2))` or `-1/2=(2a^(2))/(2a^(2))-(AC^(2))/(2a^(2))`
`:.AC=sqrt(3)a:. |v_(av)|=(sqrt(3))/((2a)/v)=(sqrt(3)v)/2`