The Position Vector of a Particle Is R(t) $t = \frac { \pi } { 4 }$

question 80

Multiple Choice

The position vector of a particle is r(t) . Find the requested vector.
-The velocity at $t = \frac { \pi } { 4 }$ for $\mathbf { r } ( \mathrm { t } ) = 4 \sec ^ { 2 } ( \mathrm { t } ) \mathbf { i } - 5 \tan ( \mathrm { t } ) \mathbf { j } + 10 \mathrm { t } ^ { 2 } \mathbf { k }$

• A) \(\mathbf { v } \left( \frac { \pi } { 4 } \right) = - 10 \mathbf { j } - 5 \pi \mathbf { k }\)
• B) \(\mathbf { v } \left( \frac { \pi } { 4 } \right) = - 10 \mathbf { j } + 5 \pi \mathbf { k }\)
• C) \(\mathbf { v } \left( \frac { \pi } { 4 } \right) = 16 \mathbf { i } - 10 \mathbf { j } + 5 \pi \mathbf { k }\)
• D) \(\mathbf { v } \left( \frac { \pi } { 4 } \right) = 16 \mathbf { i } + 10 \mathbf { j } - 5 \pi \mathbf { k }\)

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Definitions:

Average Product

The output obtained by dividing the total product by the number of units of the variable input used in production, ideally reflecting productivity per input unit.

Total Product

The total output or quantity of goods produced by a firm or economy at a given level of input.

Diminishing Returns

A principle stating that if one factor of production is increased while other factors are held constant, the incremental increases in output will eventually decrease.

Labor

The human effort, physical or mental, used in the production of goods and services.