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# 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.

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The function $$\small{s(t)}$$ describes the position of a particle moving along a coordinate line, where $$s$$ is in feet and $$t$$ is in seconds.

$$\small{s(t) = t^{3}-10t^{2}+25t+9, \qquad t \ge 0}$$

(a) Find the velocity and acceleration functions.

$$v(t)$$3t^2 - 20t + 25

$$a(t)$$6t - 20

(b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent $$\small{\infty}$$, 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 $$\small{\infty}$$, and U for the union of sets.

Interval:

(d) Over what interval(s) does the particle have positive acceleration? Use inf to represent $$\small{\infty}$$, and U for the union of sets.

Interval:

(e) Over what interval(s) does the particle have negative acceleration? Use inf to represent $$\small{\infty}$$, and U for the union of sets.

Interval:

(f) Over what interval is the particle speeding up? Slowing down? Use inf to represent $$\small{\infty}$$, and U for the union of sets.

Speeding up:

Slowing down:

Mar 30, 2022

#1
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a) correct

b)  solve    the velocity funtion > 0      3t^2 -20t+25 > 0

c)  Solve   3t^2 - 20t +20 < 0

d)  Similar to the velocity function  :   6t -20 >0

e)    6t-20 <0

f) Positive acceleration = speeding up

slowing down   acceleration < 0

Mar 30, 2022
#2
+36457
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Here is a graphical representation of the first one ( you can use the  quadratic fromula to find the roots...then test for > 0 in each of the three intervals)