A Particle Moves with Position Function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$

Multiple Choice

A particle moves with position function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$ . Find the tangential component of the acceleration vector.

A) $a _ { T } = 5 t$
B) $a _ { T } = 542 t$
C) $a _ { T } = 42 t + 5$
D) $a _ { T } = - 55 t$
E) $a _ { T } = 42 t$