A car traveling at 55 kmh hits a bridge abutment A passenger

A car traveling at 55 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 56 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger\'s upper torso, which has a mass of 34 kg? Number Units

Solution

We have

d = distance = 0.56 m
u = initial velocity = 55km/h =15.27 m/s
v = final velocity = 0 (as the passenger is brought to rest)
a =acceleration = ?

Using 3rd equation of motion: v² = u² + 2ad. This rearranges to a = (v² - u²)/2d = (0² - 15.27²)/1.12 = -208.19 m/s².

F = ma = mass x acceleration = 34 kg x -208.19 m/s² = -7078.46 N. Thus, a force of magnitude 7078.46N acts on the passenger\'s upper torso