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

question 35

Multiple Choice

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

• A) \(\mathbf { v } ( t ) = 2 \sin t \mathbf { i } - 4 \cos t \mathbf { j } + \mathbf { k }\)
• B) \(\mathbf { v } ( t ) = - 2 \cos t \mathbf { i } - 4 \sin t \mathbf { j } + 2 \mathbf { k }\)
• C) \(\mathbf { v } ( t ) = - 2 \sin t \mathbf { i } - 4 \cos t \mathbf { j } + \mathbf { k }\)
• D) \(\mathbf { v } ( t ) = - 2 \sin t \mathbf { i } + 4 \cos t \mathbf { j } + 2 t \mathbf { k }\)
• E) \(\mathbf { v } ( t ) = - 2 \cos t \mathbf { i } + 4 \sin t \mathbf { j } + \mathbf { k }\)

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