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?

Answer 1

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

Answer 2

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) ??????

Answer 3

yes it is true.

Answer 4

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