Final answer:
To find the position vector of a particle, differentiate the given position function to find the velocity function, and then integrate the velocity function to find the position function.
Step-by-step explanation:
The position vector of a particle can be found by integrating the velocity function twice. First, differentiate the given position function to find the velocity function. Then, integrate the velocity function to find the position function. In this case, the position function is given as ř(t) = 3.0t²î + 5.0ĵ - 6.0tk m. Differentiate this position function to find the velocity function. The velocity function is v(t) = 6.0tî + 5.0ĵ - 6.0k m/s. Finally, integrate the velocity function to find the position function. The position function is r(t) = 3.0t³/3î + 5.0t²/2ĵ - 6.0tk²/2 + C, where C is the constant of integration.