The Following Table Gives Coordinates of a Particle Moving Through

question 40

Multiple Choice

The following table gives coordinates of a particle moving through space along a smooth curve. $\begin{array}{|c|c|c|c|}\hline \mathbf{t} & x & y & z \\\hline 0.5 & 5.8 & 9.1 & 4.3 \\\hline 1 & 12.6 & 14.9 & 16.8 \\\hline 1.5 & 25.6 & 21.2 & 29.4 \\\hline 2 & 39.2 & 39.5 & 37.9 \\\hline 2.5 & 42.4 & 42.4 & 43 \\\hline\end{array}$

Find the average velocity over the time interval $[ 1,2 ]$ .

• A) \(v = 21.1 \mathbf { i } + 24.6 \mathbf { j } + 26.6 \mathbf { k }\)
• B) \(v = 21.1 \mathbf { i } + 26.6 \mathbf { j } + 21.1 \mathbf { k }\)
• C) \(v = 24.6 \mathbf { i } + 24.6 \mathbf { j } + 21.1 \mathbf { k }\)
• D) \(v = 26.6 \mathbf { i } + 24.6 \mathbf { j } + 21.1 \mathbf { k }\)
• E) \(v = 21.1 \mathbf { i } + 26.6 \mathbf { j } + 26.6 \mathbf { k }\)

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Definitions:

Improves

Enhances or increases in quality, value, or condition, often used in the context of health, skills, or performance.

Worsens

To degrade or deteriorate in quality, condition, or effectiveness.

Weber's Law

A principle in psychology that states the smallest change in a stimulus that can be detected is a constant proportion of the original stimulus.

Opponent-Process Theory

The theory that opposing retinal processes (red-green, yellow-blue, white-black) enable color vision. For example, some cells are stimulated by green and inhibited by red; others are stimulated by red and inhibited by green.