# What is the initial acceleration of three particle at the vertex of an equilateral triangle moving towards its neighbor?

I came across this question which, asks,

3 particles, at the corner of an equilateral triangle of side s, start moving with constant speed v, such that each always heads directly towards its clockwise neighbor. What is the magnitude of the initial acceleration of each particle?

I know what time the particles would take to meet. However acceleration seems quite a bit tricky. Also I am not hundred percent sure if the question is correct (at least in its terminology). I am still working under the assumption that the constant speed v is actually the modulus of the velocity vector.

I would be grateful if anyone can give a proper analysis of this problem, or at least check, if the problem is at all correct, that is, if the acceleration can be evaluated in terms of the length of the side and the velocity.

• It is known that the trajectory is a very well-known spiral. Instead of providing a full solution, let me throw a link. – Sangchul Lee Oct 5 '18 at 21:18
• Have you tried using polar coordinates? You can obtain expressions for the velocity and acceleration components along the radius and tangential vectors. – David Quinn Oct 5 '18 at 21:47
• Thank you I figured it out! – Nothingham Oct 6 '18 at 6:15