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 number of cycles per minute.

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 number of cycles per minute.
​
A)14 cycles/min
B)11 cycles/min
C)10 cycles/min
D)15 cycles/min
E)12 cycles/min

Quizplus · Accepted Answer

The period of the sine function in the given equation $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ is determined by the coefficient of $t$ inside the sine function. The general period of a sine function is $2\pi$, so the period of this specific function, which represents the time for one complete respiratory cycle, is given by $T = \frac{2\pi}{\pi/3} = 6$ seconds per cycle. To find the number of cycles per minute, we divide 60 seconds by the period of one cycle: $60 / 6 = 10$ cycles per minute.

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 $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$