Final answer:
The velocity of the particle at 0s is 0î - 3.0ĵ + 0 km/s and the velocity at 1.0s is 8.0î - 3.0ĵ + 6.0 km/s. The average velocity between 0s and 1.0s is 4.0î - 3.0ĵ + 2.0 km/s.
Step-by-step explanation:
The position of a particle is given by the function ř(t) = 4.0t²î - 3.0ĵ +2.0t³ km. To find the velocity of the particle at 0s and 1.0s, we can take the derivative of the position function with respect to time. Taking the derivative of ř(t), we get the velocity function v(t) = 8.0tî - 3.0ĵ + 6.0t² km/s.
Substituting t = 0 into the velocity function, we find that the velocity at 0s is v(0) = 0î - 3.0ĵ + 0 km/s. Substituting t = 1.0 into the velocity function, we find that the velocity at 1.0s is v(1.0) = 8.0î - 3.0ĵ + 6.0 km/s.
To find the average velocity between 0s and 1.0s, we can use the formula average velocity = change in position / change in time.
The change in position is given by the difference between the position function at t = 1.0 and t = 0, which is ř(1.0) - ř(0). Substituting t = 1.0 and t = 0 into the position function, we find that the average velocity between 0s and 1.0s is (4.0.1²î - 3.0ĵ +2.0.1³) - (4.0.0²î - 3.0ĵ + 2.0.0³) = 4.0î - 3.0ĵ + 2.0 km/s.