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If the acceleration of a particle in the $xy$-plane is $\langle 1-t,\ 3{ t }^{ 2 } \rangle$ and at time $t = 0$, its velocity is $\langle -2,\ 3\rangle$, find the speed of the particle at time $t = 2$.

$\sqrt {145}$

$\sqrt{117}$

$2\sqrt2$

$5\sqrt5$