Q: Circular motion problem? I am learning about circular motion and not quite sure how to approach this particular problem. Any help would be greatly appreciated!

A particle moves along a circular path over a horizontal $x$-$y$ coordinate system, at constant speed. At time $t_1 = 5$ s, it is at point ($4.00$ m, $8.00$ m) with velocity ($1.60$ m/s)$\hat{\mathbf{j}}$ and acceleration in the positive $x$ direction. At time $t_2 = 8$ s, it has velocity ($-1.6$ m/s)$\hat{\mathbf{i}}$ and acceleration in the positive $y$ direction. What are the coordinates of the center of the circular path?


A: have you tried plotting the points on paper? some tips


*

*$\hat i$ is the unit vector in the x axis. $\hat j$ for y axis.

*the magnitudes of velocity are 1.6 for both given points. we know that speed is constant. coincidence?

*the directions of these velocities are along orthogonal axes (the velocities are at right angles)

*the two points must be 90 degrees--essentially between $t_1=5$ and $t_2=8$, the particle completes a quarter circle.

*you now have enough information to calculate circumference and then radius

*use this radius to find the center of the circle using the position information given for $t_1$

