The coordinate system best suited for the motion analysis of the particle would be the polar coordinate system, which consists of the radial distance (r) and the angle from the origin (theta). Since the path of the particle is curved, the polar coordinate system would be better suited to describe its motion in terms of the radius and the angle of its position. The Cartesian coordinate system is better suited for linear motion, where the position of the particle can be described in terms of its x, y, and z coordinates. The n-t coordinate system is also known as the tangent-normal coordinate system, which is used to describe motion along a curved path, but the polar coordinate system is better suited for this particular scenario.