Use the Given Acceleration Function and Initial Conditions to Find

Multiple Choice

Use the given acceleration function and initial conditions to find the position at time t = 3. $\mathbf { a } ( t ) = 5 \cos t \mathbf { i } - 3 \sin t \mathbf { j } , \quad \mathbf { v } ( 0 ) = 8 \mathbf { j } + 5 \mathbf { k } , \quad \mathbf { r } ( 0 ) = - 5 \mathbf { i }$

A) $\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } - ( 3 \sin 3 + 15 ) \mathbf { j } + 15 \mathbf { k }$
B) $\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } + ( 3 \sin 3 - 15 ) \mathbf { j } + 15 \mathbf { k }$
C) $\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } + ( 3 \sin 3 + 15 ) \mathbf { j } + 15 \mathbf { k }$
D) $\mathbf { r } ( 3 ) = 5 \cos 3 \mathbf { i } + ( 3 \sin 3 + 15 ) \mathbf { j } + 15 \mathbf { k }$
E) $\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } + 15 \mathbf { j } + ( 3 \sin 3 + 15 ) \mathbf { k }$