(II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?

Answer

$1.9 \times 10^{4} \mathrm{N}$
$1.2 \mathrm{m}$

Christina K.

Rutgers, The State University of New Jersey

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Video Transcript

All right. So in this problem we're told that a human can survive a car crash, that's less than or equal to 30 Gs of force. So if it's maintaining under 30 Gs um of force deceleration of acceleration. I'm so sorry, I was gonna say um and we want to know first off, so one, what is the force on a 65 kg person that is decelerating at 30 Gs? So we know that force equals mass times acceleration obviously. And we have the mass. We want to know the force and we actually have the acceleration and that's 30 Gs. And that is literally 30 Times the acceleration due to gravity, which is 9.8 m/s. So if we just multiply our 65 Times 30 times 9.8 We'll get our force, which is 19,110 Newtons. And that's the standard unit for force. And then second we want to know what distance are you going to move if you are decelerating at 30GS um from 95 km/h all the way down to rest. So for this we want to find out what cinematics equation we want to use. So what do we have? We have our initial velocity, our final velocity and a distance that we want to know. We don't have any time. So that actually rules out three out of the four cinematics equations automatically. So we're left with V squared equals V, not squared plus two times the acceleration times the distance which is delta X. So we know that our V squared is equal to zero. So now we have zero equals V not squared plus to R A. Is 30 Gs. So 30 times 9.8 times delta X. And we know that our Vienna Is 95 km/h. But what is that? In meters per second? Because that's the standard for velocity. So we've got one hour equals 60 minutes times one minute, 60 seconds. Okay, we're getting somewhere within seconds And we also know that one km Is 1000 m. So if you multiply all of that out, you're going to get the speed in m per second that you're moving at is about 26 .389 meters per second. So now we can solve this. And if you just move these terms around, you'll get the delta X equals or the distance that you're going to decelerate, or the distance you're going to go before you hit rest Is equal to 1.184 meters. Mhm. Pretty simple. If you use your cinematics equations

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