Answer:
1) Velocity
[tex]v(t) = -4\cdot t^{3}+36\cdot t^{2}[/tex]
Acceleration
[tex]a(t) = -12\cdot t^{2}+72\cdot t[/tex]
2) Velocity
[tex]v(t) = -4\cdot t^{3}+24\cdot t^{2}[/tex]
Acceleration
[tex]a(t) = -12\cdot t^{2}+48\cdot t[/tex]
Step-by-step explanation:
From Physics we remember that velocity ([tex]v(t)[/tex]) and acceleration ([tex]a(t)[/tex]) are the first and second derivatives of the function position in time. That is:
1) Let [tex]s(t) = -t^{4}+12\cdot t^{3}[/tex], where [tex]t \ge 0[/tex]. The functions velocity and aceleration are, respectively:
Velocity
[tex]v(t) = -4\cdot t^{3}+36\cdot t^{2}[/tex]
Acceleration
[tex]a(t) = -12\cdot t^{2}+72\cdot t[/tex]
2) Let [tex]s(t) = -t^{4}+8\cdot t^{3}[/tex], where [tex]t\ge 0[/tex]. The functions velocity and acceleration are, respectively:
Velocity
[tex]v(t) = -4\cdot t^{3}+24\cdot t^{2}[/tex]
Acceleration
[tex]a(t) = -12\cdot t^{2}+48\cdot t[/tex]
