A block of mass 10 ~kg is moving in x -direction with a constant...

Initial K.E., $E_1=\frac{1}{2} m v^2=\frac{1}{2} \times$10 $\times($10)^2=500 $\mathrm{~J}$At $x=20 \mathrm{~m}$, retarding force, F_1=0.1 $\times$20=2 $\mathrm{~N}$At $x=30 \mathrm{~m}$, retarding force, F_2=0.1 $\times$30=3 $\mathrm{~N} \text{. }$Average Retarding Force $F=\frac{F_1+F_2}{2}=\frac{2+3}{2}=2.5$ Work done by retarding force = loss in K.E. =F $\times$s=2.5(30-20)=25 $\mathrm{~J}$Final K.E. $=E_1-\operatorname{loss}$ in K.E. $=500-25=475 \mathrm{~J}$