Question

When you sneeze, the air in your lungs accelerates from rest to 150 km/h in approximately 0.50 s. What is the acceleration of the air in m/s2 ?

Short answer

The acceleration of air while sneezing is $a=83.3m/s^2$

Step-by-step solution

Step 1. When we sneeze, our nose is irritated by dirt, infection or allergic reaction.

Our body puts all efforts to clear its airway. The diaphragm, abdominal, vocal chords, and chest muscles puts collective efforts while sneezing. Therefore, the air from our lungs accelerates at high rate.

Step 2. Before we sneeze, the air remains at rest. Therefore, the initial speed of air is considered as zero, vi→=0. 

The speed of air when we sneeze is given as 150 km/h. Therefore,

$$\begin{gathered} \overrightarrow{v_f}=150km/h \\ =\frac{150\times 1000}{3600}m/sec \\ =\frac{125}{3}m/sec \end{gathered}$$

hence, the final speed of air is $\overrightarrow{v_f}=\frac{125}{3}m/sec$

The time taken by air to reach the given speed is $t=0.50sec$

Let the acceleration of the air is represented as$a$

Step 3. Write the equation of motionvf→=vi→+atSubstitute the values of all the variables in the above equation.

$$\begin{gathered} \frac{125}{3}=0+a(0.50) \\ a=\frac{125}{3(0.50)} \\ a=\frac{125}{1.5}=83.3 \\ a=83.3m/s^2 \end{gathered}$$
Therefore, the acceleration of air while sneezing is$a=83.3m/s^2$.