$(25$ pts$)$ The crate has a mass of $80$ kg and is being towed by the towing force $P=90t^2$ N $,$ which is always directed at $20$ from the horizontal as shown. The static coefficient of friction is ${}_s=0\mathrm{.}4$ and the kinetic coefficient of friction is ${}_k=0\mathrm{.}3.$

a$.$ Determine the crate's initial acceleration

b$.$ Calculate the crate's velocity at $t=2sec$