Find the Velocity and Position Vectors of an Object with Acceleration

question 70

Short Answer

Find the velocity and position vectors of an object with acceleration $\mathbf { a } ( t ) = 4 \mathbf { i } - 72 \mathbf { j } + ( 72 t + 4 ) \mathbf { k }$ , initial velocity $\mathbf { v } ( 0 ) = \mathbf { i } + \mathbf { k }$ , and initial position $\mathbf { r } ( 0 ) = \mathbf { j } + 3 \mathbf { k }$ .

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Definitions:

Major Premise

The first premise in a syllogism, typically a general statement or proposition that asserts a universal truth or principle.

Categorical Syllogisms

A form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion, each statement being categorical.

Moods

Moods refer to the different forms of a categorical syllogism, characterized by the arrangement of the quantity and quality of its propositions.

Middle Term

The term that appears in both premises of a standard syllogism but not in the conclusion, acting as a link in deductive reasoning.