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The position of a particle for $t\geq0$ is given by the vector equation $\vec{s}=\left(t\cos{t}\right)\vec{i}+\left(t\sin{t}\right)\vec{j}$.

For the interval $\left[0, \pi\right]$ what is the maximum speed of the particle?

$3.297$

$\pi$

$2.381$

$1.391$