A particle moves horizontally in uniform circular motion, overa horizontal xy pl

Question

A particle moves horizontally in uniform circular motion, overa horizontal xy plane. At one instant it moves through thepoint with coordinates (x, y) with a velocity of v(i unit vector)and an acceleration of -a(j unit vector). In theseexpressions, v and a are the speed and the magnitude ofacceleration, respectively, and thus are positive quantities. IN TERMS OF THE GIVEN VARIABLES, what are the coordinates (a)x(initial) and (b) y(initial) of the center of the circularpath? Please explain your steps, and list what equations you use fora particular step. I rate lifesaver for a clear answer. A particle moves horizontally in uniform circular motion, overa horizontal xy plane. At one instant it moves through thepoint with coordinates (x, y) with a velocity of v(i unit vector)and an acceleration of -a(j unit vector). In theseexpressions, v and a are the speed and the magnitude ofacceleration, respectively, and thus are positive quantities. IN TERMS OF THE GIVEN VARIABLES, what are the coordinates (a)x(initial) and (b) y(initial) of the center of the circularpath? Please explain your steps, and list what equations you use fora particular step. I rate lifesaver for a clear answer.

Explanation / Answer

the radius is R note v is perpendicular to a, so a = v2/R, radius R =v2/a vector (x, y) is parallel to vector a but in opposite direction. ais along -y direction, so (x, y) is along +y direction. so x = 0, y = R = v2/a answer: (0, v2/a)

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