physics help with impulse and momentum in collisions pls!!!!!! urget?

Question

choose the air bag case with the highest initial velocity(0.55 m/s). Assume the initial kinetic energy is dissipated by the air bag and the average over-pressure is 850 Pa (Pa is an SI unit, the pascal which equals 1 N/ m^2). what volume of air (in m^3) was pushed out of the bag? pls convert the answer to cubic centimeters,
1/2 mv^2 = pv
p=pressure
v=volume
w=integral pdv.
thanks so much!!!!!!!!!

Answer 1

Assuming energy is conserved, kinetic energy 1/2 mv^2 = work w = integral(pdV), as you have given. We don't know the energy since mass isn't given. And since this isn't compression but just pumping, we assume constant p (=850) so integral(pdV) = p * deltaV. Then we can say that deltaV = 1/2 mv^2/p = 1/2 m*0.55^2/850 = 0.000178*m. Is that what you're after? Note that this answer is in m^3, so convert to cm^3.