Two blocks, A and $B,$ are initially held together by a string as shown in the figure; the mass of block $A$ is of $2$ kg and the mass of block B is $6$ kg $.$ The massless spring in$-$between the two blocks has a spring constant of $k=655\frac{N}{m}$ and is initially compressed by $45$ cm $.$ The two blocks are initially moving together with a speed of $1\mathrm{.}0\frac{m}{s}.$ When the string is cut $($i$.$e$.,$ when the blocks are released$),$ the spring expands and pushes the two blocks apart. What is the speed $($in $\frac{m}{s})$ of the block A$?$ You may assume that the surface is horizontal and frictionless. HINT: As shown in the figure, $v_A$ and $v$ must be in opposite directions $($i$.$e$.,$ have opposite sign$).$