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

question 9

Multiple Choice

$\text { For the curve } r ( t ) \text {, write the acceleration in the form aTT } + \text { anN. }$
- $$\mathbf { r } ( \mathrm { t } ) = \left( \mathrm { t } ^ { 2 } - 1 \right) \mathbf { i } + ( 2 \mathrm { t } - 3 ) \mathbf { j } + 6 \mathbf { k }$$

• A) \(a = \frac { t } { t ^ { 2 } + 1 } \mathbf { T } + \frac { 1 } { t ^ { 2 } + 1 } \mathbf { N }\)
• B) \(\mathbf { a } = \frac { 2 \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { T } + \frac { 2 } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { N }\)
• C) \(\mathbf { a } = \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { T } + \frac { 1 } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { N }\)
• D) \(\mathbf { a } = \frac { 2 t } { t ^ { 2 } + 1 } \mathbf { T } + \frac { 2 } { t ^ { 2 } + 1 } \mathbf { N }\)

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Definitions:

Exam Question

A query or problem posed during an examination to evaluate a student's knowledge or skills.

Simulation Heuristic

A cognitive heuristic where people determine the likelihood of an event based on how easily they can imagine it happening, influencing their perception of risks and outcomes.

Conformity

Going along with the crowd, that is, saying or doing whatever other people are doing.

Intentional Behavior

Actions that are performed with awareness and purpose towards achieving a specific goal.