Find the Acceleration for the Given Position Vector $\vec { r } ( t ) = \left\langle 2 t , \left( 1 + t ^ { 2 } \right) ^ { 3 } , t \right\rangle$

Multiple Choice

Find the acceleration for the given position vector, $\vec { r } ( t ) = \left\langle 2 t , \left( 1 + t ^ { 2 } \right) ^ { 3 } , t \right\rangle$

A) $\vec { a } ( t ) = \left\langle 2,6 t \left( 1 + t ^ { 2 } \right) ^ { 2 } , t \right\rangle$
B) $\vec { a } ( t ) = \left\langle 0,6 \left( 1 + t ^ { 2 } \right) ^ { 2 } + 24 t ^ { 2 } \left( 1 + t ^ { 2 } \right) , 0 \right\rangle$
C) $\vec { a } ( t ) = \left\langle 0,2 t \left( 1 + t ^ { 2 } \right) , 0 \right\rangle$
D) $\vec { a } ( t ) = \left\langle 0,6 t ^ { 2 } ( 1 + 2 t ) ^ { 2 } , 0 \right\rangle$