Respuesta :
Using integrals, it is found that the particle travels 21.25 units between t = 0 and t = 5.
How is the total distance traveled calculated?
- The total distance traveled by a particle modeled by an equation of position s(t) between t = a and t = b is given by:
[tex]D = \int_{a}^{b} s(t) dt[/tex]
In this problem, the equation that models the position of the particle is:
[tex]s(t) = t^3 - 3t^2 - 2[/tex]
Hence, applying integral properties, then the Fundamental Theorem of Calculus, we have that the distance traveled is of:
[tex]D = \int_{a}^{b} s(t) dt[/tex]
[tex]D = \int_{0}^{5} (t^3 - 3t^2 - 2) dt[/tex]
[tex]D = \frac{t^4}{4} - t^3 - 2t|_{t = 0}^{t = 5}[/tex]
[tex]D = \left(\frac{5^4}{4} - 5^3 - 2(5)\right) - \left(\frac{0^4}{4} - 0^3 - 2(0)\right)[/tex]
[tex]D = 21.25[/tex]
The particle travels 21.25 units between t = 0 and t = 5.
You can learn more about integrals at https://brainly.com/question/20733870
