(1 point) 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) = t - 14t + 49t + 3, (a) Find the velocity and acceleration functions. v(t): 3t^2-28t+49 a(t): 6t-28 (b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent o, and U for the union of sets. Interval: t0 (c) Over what interval(s) is the particle moving in the negative direction? Use inf to represent o, and U for the union of sets. Interval: (7/3,7) (d) Over what interval(s) does the particle have positive acceleration? Use inf to represent o, and U for the union of sets. Interval: (4.666, inf) (e) Over what interval(s) does the particle have negative acceleration? Use inf to represent o, and U for the union of sets. Interval: (f) Over what interval is the particle speeding up? Slowing down? Use inf to represent o, and U for the union of sets. Speeding up: Slowing down: