Question

A particle is moving with the given data. Find the position of the particle.a(t) = t² - 8t + 7

Answer 1

`s(t) = (t^4)/(12) - (4t^3)/(3) + (7t^2)/(2) + v_0t + s_0`

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 = (t^3)/(3) - 4t^2 + 7t +v_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 {((t^3)/(3) - 4t^2 +7t + v_0)} \, dt = (t^4)/(12) - (4t^3)/(3) + (7t^2)/(2) + v_0t + s_0`