A Force with Magnitude $14 \mathrm {~N}$ Acts Directly Upward from the Xy-Plane on an Object with from the Xy-Plane

Multiple Choice

A force with magnitude $14 \mathrm {~N}$ acts directly upward from the xy-plane on an object with mass 6 $\mathrm { kg }$ . The object starts at the origin with initial velocity $\mathbf { v } ( 0 ) = 7 \mathbf { i } - 2 \mathbf { j }$ . Find its position function.
Select the correct answer.

A) $\mathbf { r } ( t ) = 7 t \mathbf { i } - 2 t \mathbf { j }$
B) $\mathbf { r } ( t ) = 2 t ^ { 2 } \mathbf { i } - 7 t ^ { 2 } \mathbf { j } + 14 t ^ { 3 } \mathbf { k }$
C) $\mathbf { r } ( t ) = 2 t \mathbf { i } - 4 t \mathbf { j } + t ^ { 2 } \mathbf { k }$
D) $\mathbf { r } ( t ) = 5 t ^ { 3 } \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k }$
E) $\mathbf { r } ( t ) = 7 t \mathbf { i } - 2 t \mathbf { j } + \frac { 7 } { 6 } t ^ { 2 } \mathbf { k }$