a
\(\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,Here,\,m = 10\,kg,\,{v_i} = 10\,m\,{s^{ - 1}}\\
Initial\,kinetic\,energy\,of\,the\,block\,is\\
{K_i} = \frac{1}{2}mv_i^2 = \frac{1}{2} \times \left( {10\,kg} \right) \times {\left( {10\,m{s^{ - 1}}} \right)^2}\\
\,\,\,\,\,\, = \,500\,J\\
Work\,done\,by\,retarding\,force\\
W = \int\limits_{{x_1}}^{{x_2}} {{F_r}dx = \int\limits_{20}^{30} { - 0.1\,xdx =  - 0.1\left[ {\frac{{{x^2}}}{2}} \right]_{20}^{30}} } 
\end{array}\)

\(\begin{array}{l}
 =  - 0.1\left[ {\frac{{900 - 400}}{2}} \right] =  - 25\,J\\
According\,to\,work - energy\,theorem,\\
W = {K_f} - {K_i}\\
{K_f} = W + {K_i} =  - 25\,J + 500\,J = 475\,J
\end{array}\)