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At time t1 = 2.00 s, the acceleration of a particle in counterclockwise circular motion is (9.00i + 8.00j) m/s^2. It moves at constant speed. At time t2 = 3.00s (3/4 of a revolution later), it's acceleration is (8.00i - 9.00j) m/s^2. Find the radius of the path taken by the particle.

Constant speed implies no tangential acceleration. The acceleration is centripetal. So you know it has an angular velocity of displacement/time (solve that, you have the numbers above.)

magnitude acceleration= w^2 * r solve for r.

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