A Particle Moves with Position Vector $\vec { r } ( t ) = \ln t \vec { i } + t ^ { - 1 } \vec { j } + e ^ { - t } \vec { k }$

question 47

Multiple Choice

A particle moves with position vector $\vec { r } ( t ) = \ln t \vec { i } + t ^ { - 1 } \vec { j } + e ^ { - t } \vec { k }$ . Describe the movement of the particle as t $\rightarrow$ $\infty$ .

• A)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\) \(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive y-axis with slower and slower speed.
• B)The particle will approach the positive y-axis asymptotically as t \(\rightarrow\)\(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive x-axis with slower and slower speed.
• C)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\) \(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive x-axis with increasing speed.
• D)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\)\(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive x-axis with slower and slower speed.
• E)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\) \(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive z-axis with slower and slower speed.

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Definitions:

Investment Horizon

Investment horizon refers to the total length of time that an investor expects to hold a security or a portfolio.

Promised Yield

The return that a bond issuer indicates to the bondholder that will be received, factoring in the interest rate and the term.

Cash Flow Matching

A strategy of investing in such a way that cash flows from the investments will meet the investor's outflows when needed, often used in pension planning and managing corporate finances.

Active Bond Portfolio

A portfolio of bonds managed with the intention of outperforming the market through various strategies, such as sector rotation and duration management.