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(B) At point $P_1$,the velocity vector $\vec{v}_1$ is directed along the positive $y$-axis,so $\vec{v}_1 = v\hat{j}$.At point $P_2$,the velocity vecto

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$\sqrt{2}v$

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(B) At point $P_1$,the velocity vector $\vec{v}_1$ is directed along the positive $y$-axis,so $\vec{v}_1 = v\hat{j}$.At point $P_2$,the velocity vector $\vec{v}_2$ is directed along the negative $x$-axis,so $\vec{v}_2 = -v\hat{i}$.The change in velocity $\Delta\vec{v}$ is given by $\Delta\vec{v} = \vec{v}_2 - \vec{v}_1 = -v\hat{i} - v\hat{j}$.The magnitude of the change in velocity is $|\Delta\vec{v}| = \sqrt{(-v)^2 + (-v)^2} = \sqrt{v^2 + v^2} = \sqrt{2v^2} = \sqrt{2}v$.

$A$ particle moves with a constant speed $v$ along a circle of radius $R$. What is the change in velocity of the particle as it moves from point $P_1$ to $P_2$?

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