$3/166$ The system is initially moving with the cable taut, the $10-kg$ block moving down the rough incline with a speed of $0\mathrm{.}3\frac{m}{s},$ and the spring stretched $25$ mm $.$ By the method of this article, $($a$)$ determine the velocity $v$ of the block after it has traveled $100$ mm $,$ and $($b$)$ calculate the distance traveled by the block before it comes to rest.

Problem $3/166$