Given,
The mass of the train, m=40000 kg
The initial velocity of the train, u=0.700 m/s
The compression in the spring bumper that stopped the train, x=0.250 m
The final velocity of the train, v=0 m/s
From the equation of motion,
Where a is the acceleration of the train.
On substituting the known values,
The magnitude of the force applied by the train will be equal to the magnitude of the restoring force of the spring.
Therefore,
Where k is the spring constant of the spring.
On substituting the known values,
Therefore the spring constant of the spring is 156800 N/m
Thus the correct answer is option C.