<p>This study investigates the classic pursuit problem in classical mechanics, where particles move towards each other from the vertices of various regular polygons. Both constant velocity and constant acceleration scenarios of this problem are explored. Theoretical calculations for the constant velocity case are validated through numerical simulations. The analysis then extends to the constant acceleration case, including scenarios with non-zero initial velocities. Notably, it is found that in constant acceleration, based purely on numerical results, particles do not converge. This comprehensive analysis aims to engage high school and undergraduate students with a captivating exploration of classical mechanics.</p>