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The position of a particle for $t\geq0$ is given by the parametric equations $x=5\cos{t}$ and $y=2\sin{t}$.

For what value of $t$ in the interval $\left[0, \pi\right]$ is the distance between the particle and the origin the smallest?

$t=0$

$t=\cfrac{\pi}{4}$

$t=\cfrac{\pi}{2}$

$t=\cfrac{\pi}{8}$