Answer:
a) [tex]v(t) = 3t^{2} - 16t + 2[/tex]
b) The velocity after 3 seconds is -3m/s.
c) [tex]t = 0.13s[/tex] and [tex]t = 5.2s[/tex].
Step-by-step explanation:
The position is given by the following equation.
[tex]s(t) = t^{3} - 8t^{2} + 2t[/tex]
(a) Find the velocity at time t.
The velocity is the derivative of position. So:
[tex]v(t) = s^{\prime}(t) = 3t^{2} - 16t + 2[/tex].
(b) What is the velocity after 3 seconds?
This is v(3).
[tex]v(t) = 3t^{2} - 16t + 2[/tex]
[tex]v(3) = 3*(3)^{2} - 16*(3) + 2 = -19[/tex]
The velocity after 3 seconds is -3m/s.
(c) When is the particle at rest?
This is when [tex]v(t) = 0[/tex].
So:
[tex]v(t) = 3t^{2} - 16t + 2[/tex]
[tex]3t^{2} - 16t + 2 = 0[/tex]
This is when [tex]t = 0.13s[/tex] and [tex]t = 5.2s[/tex].
