A railcar with an overall mass of 75,000 kg traveling with a velocity vi is approaching a barrier equipped with a bumper consisting of a nonlinear spring whose force vs. compression law is given by Fs = βx3 (β = 640*106 N/m3) and x is the compression of the bumper.
Treating the system as a particle, assuming that the contact between railcar and rails is frictionless, and letting vi = 6 km/h, determine the bumper compression necessary to bring the railcar to a stop.