The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2. If you are in an automobile accident with an initial speed of 105 km/h(65 mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

Video transcript

Welcome back everybody. We are making observations about a motorcyclist who is in the middle of a race. Now we are told that while he is racing, he encounters or spots a cat in the middle of the road. As a result, he needs to decelerate and then stop A. K. A His velocity will reach zero. Now we're told at the start of his deceleration, he is traveling at a velocity of 126 kilometers an hour, but they were nice enough to convert for us. So it's really 35 m per second. Now, he achieves a magnitude of acceleration, a magnitude of acceleration of 4m/s squared. And we are tasked with finding how how much distance is covered in this time of deceleration. Now, before we start looking at any formulas, I want to look at this right here. What does this mean? He achieves a magnitude of deceleration, but does that mean that's the acceleration value we're gonna use. Well, as you see, we're going from a positive velocity value all the way to zero, meaning that our acceleration is going to have to be working against us a. K. It'll be negative four m per second squared. Great! Now that we have that and we're trying to relate acceleration, velocities and distance covered, we're going to use a kid, a magic formula. Cinematic formula states that our final velocity squared is equal to our initial velocity squared plus two times our acceleration times are desired. Distance covered. I'm going to manipulate this equation a little bit and I'm gonna subtract our initial velocity from both sides. This is going to cancel out this term and I'm going to divide both sides by two times acceleration canceling out these terms. We then get the formula that are delta S. Is equal to our final velocity squared minus our initial velocity squared all over two times our acceleration. So let's go ahead and plug in some values and find the distance cover. Our final velocity is zero squared minus our initial of squared all over two times negative four. This gives us negative 35 squared over negative eight. The negatives will cancel out becoming positive. And when you plug this into your calculator, you get 1 53.125 m are covered, which corresponds to an answer choice of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.