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 $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ ,
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​ $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ , ​
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 given function for airflow velocity is $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$. The period of a sine function $sin(Bt)$ is given by $\frac{2\pi}{B}$, where $B$ is the coefficient of $t$ inside the sine function. Here, $B = \frac{\pi}{3}$, so the period of the respiratory cycle is $\frac{2\pi}{\pi/3} = 6$ seconds. This means one full respiratory cycle takes 6 seconds.

For a Person at Rest,the Velocity V (In Liters Per v=0.85sin⁡(πt3)v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)v=0.85sin(3πt​)

For a Person at Rest,the Velocity V (In Liters Per $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$