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

question 58

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } ^ { 2 } \mathbf { r } } { \mathrm { dt } ^ { 2 } } = 3 \mathrm { t } ^ { 2 } \mathbf { i } - \mathrm { tj }$
Initial Conditions: $\left. \frac { \mathrm { d } r } { \mathrm { dt } } \right| _ { \mathrm { r } = 0 } = - 4 \mathbf { i } , \mathrm { r } ( 0 ) = 10 \mathbf { i } - 3 \mathbf { k }$

• A) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { 1 } { 4 } \mathrm { t } ^ { 4 } - 4 \mathrm { t } + 10 \right) \mathrm { i } - \frac { \mathrm { t } ^ { 3 } } { 2 } \mathrm { j } - 3 \mathrm { k }\)
• B) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { 3 } { 10 } \mathrm { t } ^ { 4 } - 4 \mathrm { t } + 10 \right) \mathrm { i } - \frac { \mathrm { t } ^ { 3 } } { 6 } \mathrm { j } - 3 \mathrm { k }\)
• C) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { 1 } { 4 } \mathrm { t } ^ { 4 } + 4 \mathrm { t } + 10 \right) \mathrm { i } + \frac { \mathrm { t } ^ { 3 } } { 6 } \mathrm { j } - 3 \mathbf { k }\)
• D) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { 1 } { 4 } \mathrm { t } ^ { 4 } - 4 \mathrm { t } + 10 \right) \mathrm { i } - \frac { \mathrm { t } ^ { 3 } } { 6 } \mathrm { j } - 3 \mathbf { k }\)

---

Definitions:

Part-Time Job

Employment with fewer hours per week than a full-time position, often offering flexibility but with fewer benefits.

Minimum-Wage

The lowest legal wage that employers can pay their workers, aimed at ensuring a basic standard of living for employees.

Social Class

Divisions in a society based on social and economic status.

First-Generation Canadian

A person born in Canada to parents who immigrated to Canada.