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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Definitions:

Financial Statement

A written record that conveys the business activities and financial performance of a company, typically including the balance sheet, income statement, and cash flow statement.

Permanent/Temporary

Refers to accounts on a company's balance sheet that are carried over from one accounting period to the next, with permanent indicating long-term accounts and temporary indicating accounts that are closed at the end of each period.

Coal Deposit

A geological formation containing a natural accumulation of coal, which can be mined for use as a fuel.

Tons Available

A measurement indicating the quantity of a commodity or material expressed in tons that is available for use or sale.