(1 point) The function s(t) describes the position of a particle moving along a coordinate line,...

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(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) = t³ - 14t² + 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: t≥0 (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: (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) = t³ - 14t² + 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: t≥0 (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:

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a Find the velocity and acceleration functions Given st t3 14t2 49t 3 To find the velocity function we take the derivative of the position function with respect to time vt st 3t2 28t 49 To find the ac... View the full answer