Chapter 4, Problem 66P

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t₁ = 4.00 s, it is at point (5.00 m, 6.00 m) with velocity $(3.00\text{m/s) <mover accent="true"> j <mo> ^ </mo> </mover>}$ and acceleration in the positive x direction. At time t₂ = 10.0 s, it has velocity $(-3.00\text{m/s) <mover accent="true"> i <mo> ^ </mo> </mover>}$ and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path if t₂ − t_l is less than one period?