Question

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

Answer 1

Answer:

$s(t) = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0$

Step-by-step explanation:

We can first integrate the acceleration to find the velocity with respect to time

$v(t) = \int {a(t)} \, dt= \int {t^2 - 8t + 7} \, dt = \frac{t^3}{3} - 4t^2 + 7t +v_0$

Then we can integrate the velocity to find the position of the particle with respect to time:

$s(t) = \int {v(t)} \, dt = \int {(\frac{t^3}{3} - 4t^2 +7t + v_0)} \, dt = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0$