Question $2(2\mathrm{.}5$ points$)$

A $60-kg$ body slides along a smooth rod BC and is connected to two springs, $S_1$ and $S_2,$ as shown in the figure. Spring $S_1$ has a spring constant of $k_1=600\frac{N}{m}$ with an unstretched length of $2\mathrm{.}0$ m $,$ while spring $S_2$ has a spring constant of $k_2=300\frac{N}{m}$ with an unstretched length of $2\mathrm{.}5$ m $.$ The body is initially at position A$,$ where it has a velocity of $3\mathrm{.}0\frac{m}{s}$ down the rod. Using the principle of work and energy, determine the velocity of the body when it reaches position $A^{\text{'}}.$

Ans: $4\mathrm{.}66\frac{m}{s}$ to the left