Space Find the Velocity $\mathbf { v } ( t )$

question 54

Multiple Choice

$\text { The position vector } \mathbf { r } ( t ) = \left( 4 \ln t , \frac { 2 } { t } , 6 t ^ { 9 } \right) \text { describes the path of an object moving in }$ space. Find the velocity $\mathbf { v } ( t )$ of the object.

• A) \(\mathbf { v } ( t ) = \frac { 4 } { t } \mathbf { i } + \frac { 4 } { t ^ { 2 } } \mathbf { j } + 54 t ^ { 8 } \mathbf { k }\)
• B)\(\mathbf { v } ( t ) = - \frac { 4 } { t } \mathbf { i } + \frac { 4 } { t ^ { 2 } } \mathbf { j } + 6 t ^ { 8 } \mathbf { k }\)
• C)\(\mathbf { v } ( t ) = - \frac { 4 } { t } \mathbf { i } + \frac { 2 } { t ^ { 2 } } \mathbf { j } + 54 t ^ { 8 } \mathbf { k }\)
• D)\(\mathbf { v } ( t ) = \frac { 4 } { t } \mathbf { i } - \frac { 2 } { t ^ { 2 } } \mathbf { j } + 54 t ^ { 8 } \mathbf { k }\)
• E)\(\mathbf { v } ( t ) = - \frac { 4 } { t } \mathbf { i } - \frac { 2 } { t ^ { 2 } } \mathbf { j } + 6 t ^ { 8 } \mathbf { k }\)

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