Question

Given an acceleration vector, initial velocity ⟨u_{0}, v_{0}, w_{0}⟩ and initial position ⟨ x_{0}, y_{0}, z_{0}⟩ find the velocity and position vectors for t≥0. a(t) = ⟨0, 0, 4⟩ , ⟨u_{0}, v_{0}, w_{0}⟩ = ⟨8, 2, 0⟩ , ⟨ x_{0}, y_{0}, z_{0}⟩ = ⟨0, 3, 0⟩ What is the velocity vector?

Answer 1

To find the velocity vector, we can integrate the acceleration vector with respect to time. Integrating the x-component of the acceleration, we get the x-component of the velocity as a function of time. Similarly, integrating the y-component and z-component of the acceleration will give us the y-component and z-component of the velocity, respectively.