The function s(t) describes theposition of a particle moving along a coordinateline, where s is in feet and t is in seconds.s(t) = t – 10t? + 25t + 6,t > 0(a) Find the velocity and acceleration functions.v(t):a(t):(b) Over what interval(s) is the particle moving inthe positive direction? Use inf to represent co,and U for the union of sets.Interval:(c) Over what interval(s) is the particle moving inthe negative direction? Use inf to represent oo,and U for the union of sets.Interval:(d) Over what interval(s) does the particle havepositive acceleration? Use inf to represent ∞,and U for the union of sets.Interval: (e) Over what interval(s) does the particle havenegative acceleration? Use inf to represent co,and U for the union of sets.Interval:(f) Over what interval is the particle speedingup? Slowing down? Use inf to represent co, andU for the union of sets.Speeding up:Slowing down:

Name: The function s(t) describes theposition of a particle moving along a
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Description: The function s(t) describes theposition of a particle moving along a coordinateline, where s is in feet and t is in seconds.s(t) = t – 10t? + 25t + 6,t > 0(a) Find the velocity and acceleration functions.v(t):a(t):(b) Over what interval(s) is the pa

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Math

Calculus

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 – 10t? + 25t + 6, t 2 0 (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 o, 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 co, and U for the union of sets. Interval: