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vaieri [72.5K]
3 years ago
12

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

Mathematics
1 answer:
Anna71 [15]3 years ago
6 0

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

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