Solving a Circular Motion Problem: Find the Center of the Path

[ubiquinone]

Hi, I'm just beginner at physics and circular motion is really a new topic for me. I came across this problem in the opening chapter exercises. I glanced at the problems following this one and many of them are pretty much the same. I was just wondering if someone could please show me how to solve this problem, so I can use this as a guide when I solve similar problems of this chapter. Thank You.

Question: A particle moves along a circular path over a horizontal $$xy$$ coordinate system, at constant speed. At time $$t_1=4.00s$$, it is at point $$(5.00m,6.00m)$$ with velocity $$(3.00m/s)\vec{j}$$ and acceleration in the positive $$x$$ direction. At time $$t_2=10.0s$$, it has velocity $$(-3.00m/s)\vec{i}$$ and acceleration in the positive $$y$$ direction. What are the coordinates of the center of the circular path?

 

[OlderDan]

If you are just picking a problem before studying circular motion, this is probably not the one to start with. If you want to take a shot at it, try to figure out where the particle is at t = 10 seconds. How far does it travel between t = 4 seconds and t = 10 seconds? How big is the circle?

 

[ubiquinone]

Hi OlderDan, thanks again for replying to my questions. No, I'm not picking random questions to do in fact this is the 4th question from my chapter exercises on circular motion. The first three were easy, straight formula calculations of solving for one of the unknows with a_c=v^2/r.
But I want to be able to solve this type of problem, as I have many similar that I need to encounter in the upcoming problems.
If you can help a little bit more, may you please offer me a hand. Thanks again for your patience.

 

[OlderDan]

Hi OlderDan, thanks again for replying to my questions. No, I'm not picking random questions to do in fact this is the 4th question from my chapter exercises on circular motion. The first three were easy, straight formula calculations of solving for one of the unknows with a_c=v^2/r.
But I want to be able to solve this type of problem, as I have many similar that I need to encounter in the upcoming problems.
If you can help a little bit more, may you please offer me a hand. Thanks again for your patience.

Then you should try to answer the questions I posed. How far does it move between t = 4s and t = 10s? Knowing the direction it is moving at both times, what part of a circle is this? How big is the circle?