The Following Table Gives Coordinates of a Particle Moving Through

question 63

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

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Definitions:

Tiny Task

A very small or minor job, duty, or responsibility.

Immediate Reward

A benefit or compensation received soon after a particular action is taken, serving as immediate gratification for that action.

Procrastinated

Delayed or postponed actions or decisions, often as a result of anxiety, fear of failure, or perfectionism.

Task

A piece of work to be done or undertaken.