Answer:
[tex]s(t) = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0[/tex]
Step-by-step explanation:
We can first integrate the acceleration to find the velocity with respect to time
[tex]v(t) = \int {a(t)} \, dt= \int {t^2 - 8t + 7} \, dt = \frac{t^3}{3} - 4t^2 + 7t +v_0[/tex]
Then we can integrate the velocity to find the position of the particle with respect to time:
[tex]s(t) = \int {v(t)} \, dt = \int {(\frac{t^3}{3} - 4t^2 +7t + v_0)} \, dt = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0[/tex]
