circular motion problem
a particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4, 4) with a velocity of -5.00 i^ m/s and an acceleration of +12.5j^ m/s2. What are the x and y coordinates of the centre of the circular path?

Question

circular motion problem
a particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4, 4) with a velocity of -5.00 i^ m/s and an acceleration of +12.5j^ m/s2. What are the x and y coordinates of the centre of the circular path?

anonymous · Answer

I found the radius of the path should be 2, from $$a=\frac{v^{2} }{r }$$

anonymous · Answer

I think the centre is right above the point because the direction of acceleration is towards j^ only
but I am not sure if this argument could lead to the answer directly
so is it (4,6) ??????

anonymous · Answer

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yes it is true.

anonymous · Answer

can I derive the answer from the displacement vector $$r(t)=x _{0} i + y_{0} j + R(\cos \omega t i + \sin \omega t j)$$ ?