F$13-2.$ If motor $M$ exerts a force of $F=(10t^2+100)N$ on the cable, where $t$ is in seconds, determine the velocity of the $25-kg$ crate when $t=4s.$ The coefficients of static and kinetic friction between the crate and the plane are ${}_s=0\mathrm{.}3$ and ${}_k=0\mathrm{.}25,$ respectively. The crate is initially at rest.