Answer:
[tex]s(t) = 2t^{3} - 2t^{2} + 5t - 9[/tex]
Step-by-step explanation:
The position is the integrative of the velocity.
We have that:
[tex]v(t) = 6t^{2} - 4t + 5[/tex]
So
[tex]s(t) = \int {v(t)} \, dt[/tex]
[tex]s(t) = \int {(6t^{2} - 4t + 5)} \, dt[/tex]
[tex]s(t) = 2t^{3} - 2t^{2} + 5t + K[/tex]
In which k is the constant of integration, which we use the initial condition to find.
s(1) = -4. So
[tex]-4 = 2*(1)^{3} - 2*(1)^{2} + 5(1) + K[/tex]
[tex]K = -9[/tex]
So
[tex]s(t) = 2t^{3} - 2t^{2} + 5t - 9[/tex]
