The motor, M$,$ pulls on the cable with a force F $=(10$ t$2+300)$ N$,$ where t is in seconds. If the $100$ kg crate is originally at rest at t $=0,$ determine its speed when t $=4$ s$.$ Neglect the mass of the cable and pulleys. $($Hint: First find the time needed to begin lifting the crate.$)$

Group of answer choices

v $=6\mathrm{.}75$m$/$s

v $=4\mathrm{.}05$m$/$s

v $=7\mathrm{.}23$m$/$s

v $=1\mathrm{.}98$m$/$s

v $=2\mathrm{.}14$m$/$s