The Position Vector of a Particle Is R(t) $t = 4$

question 127

Multiple Choice

The position vector of a particle is r(t) . Find the requested vector.
-The velocity at $t = 4$ for $\mathbf { r } ( \mathrm { t } ) = \left( 8 - 4 \mathrm { t } ^ { 2 } \right) \mathbf { i } + ( 6 \mathrm { t } + 2 ) \mathbf { j } - \mathrm { e } ^ { - 3 \mathrm { t } } \mathbf { k }$

• A) \(\mathbf { v } ( 4 ) = - 32 \mathbf { i } + 6 \mathbf { j } - 3 \mathrm { e } ^ { - 12 } \mathbf { k }\)
• B) \(\mathbf { v } ( 4 ) = - 32 \mathbf { i } + 6 \mathbf { j } + 3 \mathrm { e } ^ { - 12 } \mathbf { k }\)
• C) \(\mathbf { v } ( 4 ) = 32 \mathbf { i } + 6 \mathbf { j } + 3 \mathrm { e } ^ { - 12 } \mathbf { k }\)
• D) \(\mathbf { v } ( 4 ) = - 16 \mathbf { i } + 6 \mathbf { j } + 3 \mathrm { e } ^ { - 12 } \mathbf { k }\)

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Definitions:

Symbolic Play

A type of play in which children use objects, actions, or ideas to represent other objects, actions, or ideas.

Routine and Rituals

Established sequences of actions regularly followed; rituals often carry symbolic meaning and are practiced to establish order, tradition, or cultural significance.

Cognitive-Behavioral Therapy

A form of psychotherapy that treats problems by modifying dysfunctional emotions, behaviors, and thoughts.

Self-Stimulatory Behaviors

Repetitive movements or actions often performed for sensory feedback, commonly observed in individuals with autism.