Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = 5 \mathbf { i } - 6 \mathbf { j }$

question 69

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \left( \mathrm { t } ^ { 4 } + 5 \mathrm { t } ^ { 2 } \right) \mathbf { i } + 4 \mathrm { t } \mathbf { j }$
Initial Condition: $\mathbf { r } ( 0 ) = 5 \mathbf { i } - 6 \mathbf { j }$

• A) \(r ( t ) = \left( \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } - 6 \right) i + \left( 2 t ^ { 2 } + 5 \right) \mathbf { j }\)
• B) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { \mathrm { t } ^ { 5 } } { 5 } + \frac { 5 \mathrm { t } ^ { 3 } } { 3 } \right) \mathbf { i } + 2 \mathrm { t } ^ { 2 } \mathbf { j }\)
• C) \(r ( t ) = \left( \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } + 5 \right) i + \left( 2 t ^ { 2 } - 6 \right) \mathbf { j }\)
• D) \(r ( t ) = \left\{ \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } + 5 \right) i + \left( t ^ { 2 } - 6 \right) j\)

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Definitions:

Cognitive Processes

Cognitive processes that include the obtaining, processing, and retention of information, involving functions like perception, memory, and logical thinking.

Object Permanence

The understanding that objects continue to exist even when they cannot be observed.

Baillergeon

Refers to developmental psychologist Renee Baillergeon, known for her research in infant cognition, particularly in the areas of object permanence and physical reasoning.