For a person at rest, the velocity $\mathcal { V }$ (in liters per second) of airflow during a respira- tory cycle (the time from the beginning of one breath to the beginning of the next) is given by $v = 0.85 \sin \left( \frac { \pi t } { 5 } \right)$ where $t$ is the time (in seconds) .
(Inhalation occurs when $v > 0$ , and exhalation occurs when $v < 0$ .) Find the time for one full respiratory cycle.

Question

For a person at rest, the velocity $\mathcal { V }$ (in liters per second) of airflow during a respira- tory cycle (the time from the beginning of one breath to the beginning of the next) is given by $v = 0.85 \sin \left( \frac { \pi t } { 5 } \right)$ where $t$ is the time (in seconds).
(Inhalation occurs when $v > 0$, and exhalation occurs when $v < 0$.) Find the time for one full respiratory cycle. 
A) $5 \mathrm { sec }$
B) $13 \mathrm { sec }$
C) $11 \mathrm { sec }$
D) $12 \mathrm { sec }$
E) $10 \mathrm { sec }$

Quizplus · Accepted Answer

The time for one full respiratory cycle corresponds to the period of the sine function in the given equation. The period of a sine function $sin(Bt)$ is given by $\frac{2\pi}{B}$. Here, $B = \frac{\pi}{5}$, so the period is $\frac{2\pi}{\pi/5} = 10$ seconds. This means one full respiratory cycle takes 10 seconds.

For a Person at Rest, the Velocity V\mathcal { V }V

For a Person at Rest, the Velocity $\mathcal { V }$