Solve the Initial Value Problem $\frac { \mathrm { d } ^ { 2 } \mathbf { r } } { \mathrm { dt } ^ { 2 } } = ( 8 \mathrm { t } - 3 ) \mathbf { i }$

question 120

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } ^ { 2 } \mathbf { r } } { \mathrm { dt } ^ { 2 } } = ( 8 \mathrm { t } - 3 ) \mathbf { i }$
Initial Conditions: $\left. \frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } \right| _ { \mathrm { r } = 0 } = - \mathbf { k } , \mathrm { r } ( 0 ) = 8 \mathbf { i } + 7 \mathbf { j } + 6 \mathbf { k }$

• A) \(r ( t ) = \left( \frac { 8 } { 3 } t ^ { 3 } - 3 t ^ { 2 } + 8 \right) i + 7 j + ( 6 - t ) \mathbf { k }\)
• B) \(r ( t ) = \left( \frac { 8 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } + 8 \right) i - 7 j + ( t - 6 ) \mathbf { k }\)
• C) \( r ( t ) = \left( \frac { 4 } { 3 } t ^ { 3 } - \frac { 3 } { 2 } t ^ { 2 } + 8 \right) i + 7 j + ( 6 - t ) k\)
• D) \(r ( t ) = \left( \frac { 4 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } + 8 \right) i - 7 j + ( 6 - t ) k\)

---

Definitions:

Tariffs

Taxes levied on imported or exported goods, used to regulate trade and protect domestic industries.

Monroe Administration

The presidential term of James Monroe, the fifth President of the United States, from 1817 to 1825, noted for the Monroe Doctrine, pronouncing opposition to European colonialism in the Americas.

Political Harmony

A state of agreement and cooperation among different political factions or parties, often resulting in more effective governance.

Intellectual Capacity

The ability of an individual to think, reason, and understand, encompassing aspects like creativity, problem-solving, and memory.