The particle has the acceleration $\backslash (\backslash$mathbf$\{$a$\}($t$)=-12\backslash$mathbf$\{$k$\}\backslash ),$ initial velocity $\backslash (\backslash$mathbf$\{$v$\}(0)=\backslash$mathbf$\{$i$\}+\backslash$mathbf$\{$j$\}\backslash ),$ and initial position $\backslash (\backslash$mathbf$\{$r$\}(0)=12\backslash$mathbf$\{$i$\}\backslash ).$

Find the velocity of the particle.

$($Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

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$\backslash$mathbf$\{$v$\}($t$)=$

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Find the speed of the particle.

$($Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

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v$($t$)=$

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Find the position of the particle.

$($Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

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$\backslash$mathbf$\{$r$\}($t$)=\backslash$square

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