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,
[tex]v^2-u^2=2ax[/tex]
Where a is the acceleration of the train.
On substituting the known values,
[tex]\begin{gathered} 0-0.700^2=2a\times0.250 \\ \Rightarrow a=\frac{-0.700^2}{2\times0.25} \\ =-0.98\text{ m/s}^2 \end{gathered}[/tex]
The magnitude of the force applied by the train will be equal to the magnitude of the restoring force of the spring.
Therefore,
[tex]\begin{gathered} m|a|=kx \\ \Rightarrow k=\frac{m|a|}{x} \end{gathered}[/tex]
Where k is the spring constant of the spring.
On substituting the known values,
[tex]\begin{gathered} k=\frac{40000\times0.98}{0.250} \\ =156800\text{ N/m} \end{gathered}[/tex]
Therefore the spring constant of the spring is 156800 N/m
Thus the correct answer is option C.
