When you sneeze, the air in your lungs accelerates from rest to 150 km/h in approximately 0.50 s. What is the magnitude of the acceleration of the air in m/s^2

Video transcript

Hey everyone. Welcome back in this problem. A nozzle of a pressurized chamber is opened suddenly the gassing, the nozzle speeds up from rest to 350 kilometers per hour. And about 0.85 seconds were asked to determine the absolute value of the acceleration of the gas in meters per second squared. The answer choices were given are a 97. m/s squared. B 412 m per second squared, see 82.6 m per second squared or D 114 m per second squared. So we're getting some information about um speed here, about time. We want to find information about the acceleration. So let's go ahead and write down the information. We know we know that the initial speed V not, is going to be zero m per second since it's at rest pressurized chamber is open suddenly. So it goes from rest To the final speed which we're told is 350 km/h. We want to find the acceleration A And we're told that we go from rest to 350 km/h and 0.85 seconds. And so the time T is going to be 0.85 seconds. Now of the five variables we have for Arcana Matic equations, we also have delta X and we aren't given any information about that and that's not what we're trying to find. So we have three known values. One thing we're trying to find which is the acceleration. So we can go ahead and just plug this into the correct cinematic equation. And we're gonna choose the equation that doesn't include delta X because we don't have information about that value. Now, before we get started there, the final velocity, final speed we're given is in kilometers per hour. We know that we want our acceleration in meters per second squared. So let's go ahead and convert this speed two m per 2nd 1st. Now to do that, we're gonna multiply By m per kilometer. Okay. When we do that, the unit of kilometer will cancel. And we're left with just 1000 sorry, 1000 m times 350. Then we're gonna multiply by one hour divided by 60 minutes. K one hour per 60 minutes, the unit of our will cancel. We're going to be left with the unit of per minute And we can multiply one minute divided by 60 seconds, okay, one minute per 60 seconds the unit of minute will cancel. And so altogether we're left with just the units of meters per second, which is what we want. And this is going to give us a value of 97. repeated meters per second. Alright, so we have that final velocity or the final speed in the correct units. Now, now we can go ahead and use our kid a Matic equation. And again, we're choosing the one without delta accident, we get V F is equal to V naught plus the acceleration multiplied by the time T substituting in our values 97.22 repeated meters per second Is equal to 0m per second plus acceleration. A multiplied by 0.85 seconds. And so our acceleration a if we isolate for it is going to be equal to 97.2, 2 repeated meters per second divided by 0.85 seconds. We have meters per second divided by second. That's going to give us the unit of meters per second square that the question asked us to use. And we get a value of .3, m/s squared. We're gonna round to three significant digits. Like the answer does that is gonna give us an acceleration of 114 m per second squared. If we compare that with the answer choices, we see that that matches with answer choice. D thanks everyone for watching. I hope this video helped you in the next one.