Find $\mathbf { r } ( t )$ Satisfying the Conditions For

question 9

Multiple Choice

Find $\mathbf { r } ( t )$ satisfying the conditions for $\mathbf { r } ^ { \prime } ( t ) = 5 \mathbf { i } + 8 t \mathbf { j } - 6 t ^ { 2 } \mathbf { k }$ $\mathbf { r } ( 0 ) = \mathbf { i } + \mathbf { j }$

• A) \(( 5 t + 1 ) \mathbf { i } + \left( 4 t ^ { 2 } + 1 \right) \mathbf { j } - 2 t ^ { 3 } \mathbf { k }\)
• B) \(( 5 t + 1 ) \mathbf { i } + \left( 8 t ^ { 2 } + 1 \right) \mathbf { j } - 6 t ^ { 3 } \mathbf { k }\)
• C) \(5 t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } - 2 t ^ { 3 } \mathbf { k }\)
• D) \(5 t \mathbf { i } + 8 t ^ { 2 } \mathbf { j } - 6 t ^ { 3 } \mathbf { k }\)

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Definitions:

Two-factor Theory

A psychological theory that posits that emotions are based on two factors: physiological arousal and cognitive labeling of that arousal.

Schachter-Singer Theory

A theory of emotion that states emotions are determined by physiological arousal and its interpretation, based on environmental cues.

Cannon-Bard Theory

A theory of emotion that proposes emotions and physiological responses occur simultaneously and independently.

Cognitive Label

The identification or interpretation of a feeling once physiological arousal has occurred.