Find the Velocity and Position Vectors of an Object with Acceleration

question 46

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 $r ( 0 ) = \mathbf { j } + 3 \mathbf { k }$ .

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Definitions:

ACTH

Adrenocorticotropic Hormone, a pituitary hormone that stimulates the production of cortisol from the adrenal cortex.

Adenohypophysis

The anterior lobe of the pituitary gland responsible for secreting several key hormones that regulate various physiological processes.

Prostaglandin

Class of physiologically active substances present in many tissues; among its effects are vasodilation, stimulation and contraction of uterine smooth muscle and the promotion of inflammation and pain.

Glucocorticoids

These are a class of corticosteroids that play a role in glucose metabolism, anti-inflammatory processes, and immune system modulation.