Final answer:
The acceleration of the airbag can be estimated using the kinematic equation s = ut + (1/2)at^2, which, given the airbag expands 20 cm in 19 ms, results in an acceleration of approximately 104.7 m/s^2.
Step-by-step explanation:
The student is asking to estimate the acceleration of an airbag which deploys in 19 milliseconds (ms) and expands 20 cm during this time. To estimate this acceleration, we can use kinematic equations that relate displacement, time, and acceleration. From the given options, we can use the equation for final velocity to find the correct acceleration value.
First, we note that 19 ms is 0.019 seconds and 20 cm is 0.2 meters. We then use the equation v2 = u2 + 2as, where v is the final velocity, u is the initial velocity (zero in this case as the airbag starts from rest), a is acceleration, and s is displacement. Assuming the final velocity is achieved at 0.2 meters and initial velocity is zero, we have:
0 = 0 + 2a(0.2 meters)
This simplifies to:
a = 0 / (2*0.2 meters) = 0 m/s2
However, this would imply no acceleration, which is incorrect. Therefore, we need to consider the time during which the displacement occurs to compute the correct acceleration. The actual kinematic equation that would give us the acceleration assuming constant acceleration from rest is:
s = ut + (1/2)at2
Substituting the known values, we get:
0.2 = (0)0.019 + (1/2)a(0.019)2
A simple rearrangement gives us:
a = 2s / t2 = 2*0.2 / (0.019)2 = 110.5 m/s2
From the given options, the closest is b) 104.7 m/s2.