The system shown is initially moving with the

cable taut, and the $10$ kg block moving down the

rough inclined plane with a speed of $0\mathrm{.}3\frac{m}{s}.$ At

this instant in time the springs $1$ and $2$ have a

deflection of $25$ mm and $50$ mm $,$ respectively, from

their static equilibrium positions. The value of the

spring constants are $k_1=200\frac{N}{m}$ and $k_2=100$

$\frac{N}{m},$ and the coefficient of kinetic friction between

the block and the incline is $=0\mathrm{.}15.$ Using the

principles of work$-$energy, $($a$)$ determine the velocity

$v$ of the block after it has traveled $100$ mm distance

down the incline, and $($b$)$ calculate the distance

traveled by the block before it comes to rest. Both

the springs have negligible mass, and the pulleys are

massless and frictionless. Take $g=9\mathrm{.}8\frac{m}{s^2}(12+12)$