Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 68

A cat rides a merry-go-round turning with uniform circular motion. At time \( t_1 = 2.00 \text{ s} \), the cat’s velocity is \( \vec{v}_1 = (3.00 \text{ m/s})\hat{i} + (4.00 \text{ m/s})\hat{j} \), measured on a horizontal \( xy \) coordinate system. At \( t_2 = 5.00 \text{ s} \), the cat’s velocity is \( \vec{v}_2 = (-3.00 \text{ m/s})\hat{i} + (-4.00 \text{ m/s})\hat{j} \). What are (a) the magnitude of the cat’s centripetal acceleration and (b) the cat’s average acceleration during the time interval \( t_2 - t_1 \), which is less than one period?