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

---

Definitions:

Impaired Gas Exchange

A condition where there is a problem with the transfer of oxygen and carbon dioxide between the lungs and the bloodstream.

Heart Rate

The number of times the heart beats per minute, indicating cardiovascular health.

Activity Intolerance

A reduced capacity to endure physical exertion, often due to health issues, leading to fatigue or discomfort when performing activities.

Hospital-Acquired Pneumonia

An infection of the lungs that occurs during a hospital stay, often caused by bacteria that are more resistant to antibiotics.