Answer
$r = 11 i + 2 j + 21 k$ ft
Work Step by Step
$a=6t i + 12t^2 k$
$\int_0^v dv=\int_0^t (6ti + 12t^2 k) dt$
$v=3t^2 i + 4t^3 k$
$\int_{r_0}^r dr = \int_0^t (3t^2 i + 4t^3 k) dt$
$r-(3i+2j+5k)=t^3 i + t^4 k$
When $t=2$ s,
$r = 11 i + 2 j + 21 k$ ft
