Aparticle moves horizontally in uniform circular motion, over a horizontal xy plane. at one instant, it moves through the point at coordinates (3.20 m, 3.50 m) with a velocity of –2.50 i^ m/s and an acceleration of +11.6 j^ m/s2. what are the (a) x and (b) y coordinates of the center of the circular path?

We have that for the Question " the(a) x and y coordinates of the center of the circular path" it can be said that the x and y ordinates are

From the question we are told

Generally the equation for the  Acceleration is mathematically given as

Hence

We have the center at

C= (4.60, (0.95 + 3.10))

C= (4.60, 4.05)

Therefore

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since centripetal acceleration is always towards the center of the circle

so at the given position where speed and acceleration is given the center coordinate will be towards the center of circle

also we know that

so the coordinates of the center will be

so the coordinate is (3.20 m, 4.04 m)

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