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:

Private Goods

Goods that are excludable and rival in consumption, meaning their use is limited to paying customers and one person's use of the good prevents another's use of it.

Prices

The sum of money needed to buy a product or service.

Efficient Allocation

The optimal distribution of resources in an economy, where resources are utilized in a manner that maximizes societal welfare without any wastage.

Rival in Consumption

A characteristic of a good whereby one person's consumption reduces the availability of the good for another person.