For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs during a respiratory cycle is given by $0.9 \sin \frac { \pi t } { 7 }$ , where t is the time in seconds. Inhalation occurs when $v 0$ and exhalation occurs when $v

Question

For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs during a respiratory cycle is given by $0.9 \sin \frac { \pi t } { 7 }$ , 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) $14 \pi$ seconds
B) $\pi$ seconds
C)14 seconds
D) $2 \pi$ seconds
E)7 seconds

Quizplus · Accepted Answer

The period of a sine function of the form $a \sin(bx)$ is given by $\frac{2\pi}{b}$. Here, $b = \frac{\pi}{7}$, so the period is $\frac{2\pi}{\pi/7} = 14$ seconds. This period represents the time for one full respiratory cycle.

For a Person at Rest, the Velocity V (In Liters 0.9sin⁡πt70.9 \sin \frac { \pi t } { 7 }0.9sin7πt​

For a Person at Rest, the Velocity V (In Liters $0.9 \sin \frac { \pi t } { 7 }$