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) \(r ( t ) = \left( \frac { 4 } { 3 } t ^ { 3 } + \frac { 3 } { 2 } t ^ { 2 } + 8 \right) i - 7 j + ( 6 - t ) k\)

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