Find the Speed of a Particle with the Given Position $$\mathbf { r } ( t ) = 4 \sqrt { 2 } t \mathbf { i } + e ^ { 4 t } \mathbf { j } - e ^ { - 4 t } \mathbf { k }$$

question 9

Multiple Choice

Find the speed of a particle with the given position function.
$$\mathbf { r } ( t ) = 4 \sqrt { 2 } t \mathbf { i } + e ^ { 4 t } \mathbf { j } - e ^ { - 4 t } \mathbf { k }$$

• A) \(| v ( t ) | = \sqrt { 4 + 4 e ^ { t } + 4 e ^ { - t } }\)
• B) \(| v ( t ) | = \left( e ^ { 4 t } + e ^ { - 4 t } \right)\)
• C) \(| v ( t ) | = \sqrt { 4 + e ^ { 4 t } + e ^ { - 40 t } }\)
• D) \(| v ( t ) | = 4 \left( e ^ { 4 t } + e ^ { - 4 t } \right)\)
• E) \(| v ( t ) | = 4 \left( e ^ { t } + e ^ { - t } \right)\)

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Definitions:

MP

In logic, MP refers to Modus Ponens, a form of argument that if a conditional statement ('If P then Q') is accepted, and P is affirmed, then Q must also be affirmed.

MT

An abbreviation or shorthand for Modus Tollens, a logical argument form.

Inference Forms

Standard logical structures that outline the relationship between premises and conclusion, guiding the derivation of the latter from the former.

MP

A shorthand for "Member of Parliament," a representative elected to the legislative body of a country. Alternatively, in logic, it could stand for "Modus Ponens," a form of argument where from premises "If P, then Q" and "P," one concludes "Q."