A Force with Magnitude $12$ N Acts Directly Upward from the Xy-Plane on an Object

Multiple Choice

A force with magnitude $12$ N acts directly upward from the xy-plane on an object with mass $2$ kg. The object starts at the origin with initial velocity $\mathbf { v } ( 0 ) = 3 \mathbf { i } - 2 \mathbf { j }$ . Find its position function.

A) $\mathbf { r } ( t ) = 2 t ^ { 2 } \mathbf { i } - 3 t ^ { 2 } \mathbf { j } + 12 t ^ { 3 } \mathbf { k }$
B) $\mathbf { r } ( t ) = 2 t \mathbf { i } - 4 t \mathbf { j } + t ^ { 2 } \mathbf { k }$
C) $\mathbf { r } ( t ) = 3 t \mathbf { i } - 2 t \mathbf { j } +$ $3$ $\text { k }$
D) $\mathbf { r } ( t ) = 3 t \mathbf { i } - 2 t \mathbf { j }$
E) $\mathbf { r } ( t ) = 5 t ^ { 3 } \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k }$