Find the Scalar Tangential and Normal Components of Acceleration of a Particle

question 61

Multiple Choice

Find the scalar tangential and normal components of acceleration of a particle with position vector $\mathbf { r } ( t ) = e ^ { t } ( \cos 8 t , \sin 8 t , 8 )$

• A) \(a _ { \mathbf { T } } = \sqrt { 65 } e ^ { t }\) , \(a _ { \mathrm { N } } = 8 \sqrt { 65 } e ^ { t }\)
• B) \(a _ { \mathbf { T } } = 8 \sqrt { 65 } e ^ { t }\) , \(a _ { \mathrm { N } } = \sqrt { 65 } e ^ { t }\)
• C) \(a _ { \mathbf { T } } = 65 e ^ { t }\) , \(a _ { \mathrm { N } } ( t ) = 8 e ^ { t }\)
• D) \(a _ { \mathbf { T } } = 8 e ^ { t }\) , \(a _ { \mathrm { N } } = 65 e ^ { t }\)

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Definitions:

Tertiary Circular Reactions

A stage in Jean Piaget's theory of cognitive development, occurring roughly between 12 and 18 months, characterized by the purposeful adaptation of established schemes to new situations.

Secondary Circular Reactions

A developmental stage in infants marked by the repetition of actions that produce interesting outcomes, demonstrating an emerging awareness of cause and effect.

Intentionality

The quality of mental states (such as beliefs, desires, hopes, and fears) that are directed at or about situations, objects, or states of affairs.

Object Permanence

The understanding that objects continue to exist even when they cannot be seen, heard, or touched.