Running around

Six particles are located at the vertices of a regular hexagon of side length a . a. At t = 0 , t=0, they start moving simultaneously with constant speed v . v. The first particle is heading for the second, the second particle is heading for the third, and so on. Then the acceleration of each particle at t = a 2 v t=\frac { a }{ 2v } is 2 3 v 2 k a . \frac { 2\sqrt { 3 } { v }^{ 2 } }{ ka }.

Find k . k.


The answer is 3.

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