A pilot who accelerates at more than 4g begins to 'gray out' but doesn't completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (Use 331 m/s for the speed of sound in cold air.)

Video transcript

Welcome back everybody. We are given a Formula One racer who wishes to achieve a constant acceleration of three m per second. Square also achieved a final velocity of kilometers per hour. We're told he starts out with initial velocity of zero m per second And we want to figure out the shortest time in which he can achieve these values. Now before working with these, I'm gonna go ahead and make sure everything is in the same units are workable units, so we need to convert this km/h to meters per second. So within one km There is 1000 m Within one hour there is 60 minutes. Within one minute there is 60 seconds. All of these units are going to cancel out leaving us with our desired meters per second. And when you multiply and divide everything, you get that our final velocity is equal to 83.33 m per second. Now that we have all of these terms and we're trying to find T. Let's use a cinematic equation to find it. So you're given that our final velocity is equal to our initial velocity plus acceleration times, time plugging in some values here we get that our final velocity of 83.33 m per second is equal to our initial velocity of zero plus our acceleration of three times. T. T is equal to 83.33, divided by three is equal to 27.77 seconds, which is our final answer corresponding to answer choice. Thank you guys so much for watching. I hope this video helped, and we will see you all in the next one.