$\begin{array}{1 1}37cm\\38cm\\36cm\\35cm\end{array} $

Answer : 37 cm

The work done by the spring force on the block as the spring is compressed a distance $d$ from its rest state is given by

$W_s=-\large\frac{1}{2}$$kd^2$

The change in the kinetic energy of the block as it is stopped is

$\Delta K =K_f-K_i$

$\;\;\quad= 0-\large\frac{1}{2}$$mv^2$

The work-energy theorem requires that these two quantities be equal.Setting them so

$W_s=\Delta K$

$\Rightarrow -\large\frac{1}{2}$$kd^2$

$\Rightarrow -mv^2$

$d=v\sqrt{\large\frac{m}{k}}$

$\;\;\;=3.7m/s(15kg/1500N/m)^{\large\frac{1}{2}}$

$d=0.37m=37cm$

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