For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by $\pi$ $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ ,

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 v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by $\pi$ $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ ,
 
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)7 sec
B)9 sec
C)3 sec
D)8 sec
E)6 sec

Quizplus · Accepted Answer

The respiratory cycle is completed when the sine function completes one full cycle, which happens every $2\pi$ radians. Given the equation $v = 0.85 \sin \left( \frac{\pi t}{3} \right)$, we set the argument of the sine function equal to $2\pi$ to find the period of one full respiratory cycle: $\frac{\pi t}{3} = 2\pi$. Solving for $t$ gives $t = 6$ seconds, indicating that one full respiratory cycle takes 6 seconds.

For a Person at Rest, the Velocity V (In Liters π\piπ

For a Person at Rest, the Velocity V (In Liters $\pi$