Complete each problem in the space provided; show all work in logical$,$ detailed form and box in numerical answers. Include a diagram wherever possible. On any problem where an FBD is appropriate, it must be included for maximum credit. All numerical results should be stated to $3\mathrm{.}00$ or $4\mathrm{.}000$ significant figures and in mks units unless otherwise noted.

Given vec$(v)=(12\frac{(m)}{(s)})cos(4t\frac{1}{(s)})hat()-(8\frac{(m)}{s^5})t^4$hat$()+(10\frac{(m)}{(s)})widehat(k)$ where vec$(s)=(3\mathrm{.}50m)hat()$ when $t=1\mathrm{.}00s,$ determine the displacement and acceleration as functions of time.