A railcar with an overall mass of 75,000 kg traveling with a velocity υi is approaching a...

A railcar with an overall mass of 75,000 kg traveling with a velocity υi is approaching a barrier equipped with a bumper constisting of a nonlinear spring whose force vs. compression law is given by Fs = βx3,where β = 640 × 106 N/m3 and x is the compression of the bumper.

Figure P3.31

Treating the system as a particle, assuming that the contact between the railcar and rails is frictionless, and letting υi = 6 km/h, determine how long it takes for the bumper to bring the railcar to a stop.