A Particle Moves with Position Function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 6 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$

Multiple Choice

A particle moves with position function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 6 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$
Find the tangential component of the acceleration vector. Select the correct answer.

A) $a _ { T } = 6 t$
B) $a _ { T } = 42 t$
C) $a _ { T } = 42 t + 6$
D) $a _ { T } = 642 t$
E) $a _ { T } = - 66 t$