A beam $AC,$ with a sliding support at A and a roller support at $C,$ is subjected to a distributed load acting over one$-$half of the length as shown in figure below. The beam has flexural rigidity EI $=2000$ kip $-f{t}^2$ and the length of the beam is $10ft.$ Determine:

a$.$ The peak intensity $q_0$ if the maximum displacement of the beam at $A$ is ${}_{\text{m}\text{a}\text{x}}=0\mathrm{.}125$ in$.$

b$.$ The angle of rotation at $C,{}_c$; at the load condition from part a$.($positive $CCW)$