$\text { For the curve } r ( t ) \text {, write the acceleration in the form aTT } + \text { anN. }$
-$$\mathbf { r } ( \mathrm { t } ) = \frac { 4 } { 3 } ( 1 + \mathrm { t } ) ^ { 3 / 2 } \mathbf { i } + \frac { 4 } { 3 } ( 1 - t ) ^ { 3 / 2 } \mathbf { j } + 1 \mathrm { t } \mathbf { k }$$
A) $a = 1 \sqrt { \frac { 2 } { 1 - t ^ { 2 } } } T$
B) $a = 1 \sqrt { \frac { 2 } { 1 - t ^ { 2 } } } \mathbf { N }$
C) $\mathbf { a } = \mathbf { T } + 1 \sqrt { \frac { 2 } { 1 - \mathrm { t } ^ { 2 } } } \mathbf { N }$
D) $\mathbf { a } = \frac { 1 } { 3 } \sqrt { \frac { 1 } { 1 - t ^ { 2 } } } \mathbf { N }$

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The Answer of $\text { For the curve } r ( t ) \text {, write the acceleration in the form aTT } + \text { anN. }$
-$$\mathbf { r } ( \mathrm { t } ) = \frac { 4 } { 3 } ( 1 + \mathrm { t } ) ^ { 3 / 2 } \mathbf { i } + \frac { 4 } { 3 } ( 1 - t ) ^ { 3 / 2 } \mathbf { j } + 1 \mathrm { t } \mathbf { k }$$
A) $a = 1 \sqrt { \frac { 2 } { 1 - t ^ { 2 } } } T$
B) $a = 1 \sqrt { \frac { 2 } { 1 - t ^ { 2 } } } \mathbf { N }$
C) $\mathbf { a } = \mathbf { T } + 1 \sqrt { \frac { 2 } { 1 - \mathrm { t } ^ { 2 } } } \mathbf { N }$
D) $\mathbf { a } = \frac { 1 } { 3 } \sqrt { \frac { 1 } { 1 - t ^ { 2 } } } \mathbf { N }$

For the curve r(t), write the acceleration in the form aTT + anN. \text { For the curve } r ( t ) \text {, write the acceleration in the form aTT } + \text { anN. } For the curve r(t), write the acceleration in the form aTT + anN.

$\text { For the curve } r ( t ) \text {, write the acceleration in the form aTT } + \text { anN. }$