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Kinematics Problem

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Three particles A,B,C are situated at vertices of a equilateral triangle ABC of side ‘a’ m at t=0 Each of the particle moves with constant speed ‘ v ‘. A always has it’s velocity along AB ,B always has it’s velocity along BC , C always has it’s velocity along CA. Derive the equation of trajectory of any one particle (means find y=f(x) i.e. relation between y and x coordinates of the particle). Also find the rate of rotation of the triangle formed by joining the lines connecting the three points as a function of time. If you think it requires more information such as acceleration etc., introduce them if needed.
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