A particle moves horizontally in uniform circular motion, over a horizontal xy p

Question

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00

^i

m/s and an acceleration of + 12.5

^j

m/s². What are the x and y coordinates of the center of the circular path?

Options:

A . (4, 6)

B . (4, 2)

C . (2, 4)

D . (6, 4)

Answer: Option A
:
A

A Particle Moves Horizontally In Uniform Circular Motion, Ov...

since

a_{c}

points in y direction that means centre should be right above it
We know

a_{c}

\frac{v^{2}}{R}

12.5 = \frac{(2)^{2}}{R}

\Rightarrow R = 2

\Rightarrow

The centre is 2 units above the point(4,4)

\Rightarrow

Coordinates of centre =(4,6)

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