+73 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:
+37153 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
+37153 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)
https://www.desmos.com/calculator/5advoaevql
