One possible answer is: √20 ≈ 4.472
Answer:
ok its 496
Step-by-step explanation:
Answer:
![s(t) = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cfrac%7Bt%5E4%7D%7B12%7D%20-%20%5Cfrac%7B4t%5E3%7D%7B3%7D%20%2B%20%5Cfrac%7B7t%5E2%7D%7B2%7D%20%2B%20v_0t%20%2B%20s_0)
Step-by-step explanation:
We can first integrate the acceleration to find the velocity with respect to time
![v(t) = \int {a(t)} \, dt= \int {t^2 - 8t + 7} \, dt = \frac{t^3}{3} - 4t^2 + 7t +v_0](https://tex.z-dn.net/?f=v%28t%29%20%3D%20%5Cint%20%7Ba%28t%29%7D%20%5C%2C%20dt%3D%20%5Cint%20%7Bt%5E2%20-%208t%20%2B%207%7D%20%5C%2C%20dt%20%3D%20%5Cfrac%7Bt%5E3%7D%7B3%7D%20-%204t%5E2%20%2B%207t%20%2Bv_0)
Then we can integrate the velocity to find the position of the particle with respect to time:
![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](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cint%20%7Bv%28t%29%7D%20%5C%2C%20dt%20%3D%20%5Cint%20%7B%28%5Cfrac%7Bt%5E3%7D%7B3%7D%20-%204t%5E2%20%2B7t%20%2B%20v_0%29%7D%20%5C%2C%20dt%20%3D%20%5Cfrac%7Bt%5E4%7D%7B12%7D%20-%20%5Cfrac%7B4t%5E3%7D%7B3%7D%20%2B%20%5Cfrac%7B7t%5E2%7D%7B2%7D%20%2B%20v_0t%20%2B%20s_0)
you have to subtract because it says "less than" . 11-3 equals 8. Hope this helps! (: