A Particle Moves on a Straight Line with Velocity Function $v ( t ) = \sin \omega t \cos ^ { 3 } a t$

question 103

Multiple Choice

A particle moves on a straight line with velocity function $v ( t ) = \sin \omega t \cos ^ { 3 } a t$ . Find its position function $s = f ( t )$ if $f ( 0 ) = 0$ .

• A) \(\frac { \cos ^ { 5 } \omega t + 1 } { 5 \omega }\)
• B) \(\frac { \sin ^ { 2 } \omega t + 1 } { 7 a }\)
• C) \(\frac { \sin ^ { 3 } \omega t - 1 } { 3 \omega }\)
• D) \(\frac { 1 - \cos ^ { 4 } a t } { 4 a }\)
• E) \(\frac { 1 - \cos ^ { 6 } a t + 1 } { 6 a }\)

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Definitions:

Arteriosclerosis

The thickening, hardening, and loss of elasticity of the walls of arteries, often leading to restricted blood flow.

Tunica Intima

The innermost layer of a blood vessel, composed of a thin layer of endothelial cells that lines the interior surface.

Tunica Media

The tunica media is the middle layer of the wall of blood vessels and lymphatic vessels, consisting predominantly of smooth muscle cells and elastic tissue, contributing to vascular tone and blood flow regulation.

Endothelium

A thin layer of cells lining the blood and lymphatic vessels, heart, and some other body cavities.