Need steps and answer, please.

The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(t)=t32t2+t+7,t0 (a) Find the velocity and acceleration functions. v(t):a(t): (b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent , and U for the union of sets. Interval (c) Over what interval(s) is the particle moving in the negative direction? Use inf to represent , and U for the union of sets. Interval (d) Over what interval(s) does the particle have positive acceleration? Use inf to represent , and U for the union of sets. Interval (e) Over what interval(s) does the particle have negative acceleration? Use inf to represent , and U for the union of sets. Interval (f) Over what interval is the particle speeding up? Slowing down? Use inf to represent , and U for the union of sets. Speeding up: Slowing down