$\text { What force is required so that a particle of mass } m \text { has the following position function? }$

question 47

Multiple Choice

$\text { What force is required so that a particle of mass } m \text { has the following position function? }$ $$\mathrm { r } ( t ) = 5 t ^ { 3 } \mathbf { i } + 10 t ^ { 2 } \mathbf { j } + 7 t ^ { 3 } \mathbf { k }$$

• A) \(\mathrm { F } ( t ) = 30 m t \mathbf { i } + 20 m \mathbf { j } + 42 m t \mathbf { k }\)
• B) \(\mathrm { F } ( t ) = 30 m t ^ { 2 } \mathbf { i } + 20 m \mathbf { j } + 42 m t \mathbf { k }\)
• C) \(\mathrm { F } ( t ) = 42 m t \mathbf { i } + 42 m \mathbf { j } + 20 m t \mathbf { k }\)
• D) \(\mathrm { F } ( t ) = m t ^ { 2 } \mathbf { i } + 5 m t \mathbf { j } + 10 m t ^ { 2 } \mathbf { k }\)
• E) \(\mathrm { F } ( t ) = 30 m t \mathbf { i } + 20 \mathrm {~m} \mathbf { j } + t \mathbf { k }\)

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Definitions:

Unauthorized Contract

A contract made by a person who lacks the authority to do so, potentially making it unenforceable against the presumed principal.

Torts

Civil wrongdoings recognized by law as grounds for a lawsuit, resulting in injury or harm to someone and constituting the basis for a claim by the injured party.

Misrepresent

To provide false or misleading representation of facts, often with the intention to deceive.

Independent Contractor

An individual or entity contracted to perform work for another entity as a non-employee, offering services to the public.