Find the Speed of a Particle with the Given Position $\mathrm { r } ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 3 t ^ { 6 } \mathbf { k }$

question 57

Multiple Choice

Find the speed of a particle with the given position function. $\mathrm { r } ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 3 t ^ { 6 } \mathbf { k }$

• A) \(| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t ^ { 2 } + 100 t ^ { 10 } }\)
• B) \(| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t + 324 t ^ { 9 } }\)
• C) \(| \mathbf { v } ( t ) | = 1 + 100 t ^ { 2 } + 324 t ^ { 10 }\)
• D) \(| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t ^ { 2 } + 324 t ^ { 10 } }\)
• E) \(| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t + t ^ { 9 } }\)

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