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

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:

Representative Clade

A group of organisms that includes an ancestor and all of its descendants, representing a single branch on the tree of life.

Supergroup

In biology, a high-level classification rank above kingdom, used in some recent taxonomic systems to organize the diversity of life.

Trypanosomes

Single-celled parasitic organisms responsible for diseases like African sleeping sickness and Chagas' disease, transmitted by insect vectors.

Foraminiferans

Single-celled protists with shells, known for their role in marine ecosystems and as indicators of environmental change.