Final answer:
To find the particle's velocity given an acceleration of a(t) = 3k and initial velocity v(0) = 16i - 3j, we integrate the acceleration and apply the initial condition, resulting in v(t) = 3kt + (16i - 3j).
Step-by-step explanation:
To find the velocity of a particle with the given acceleration function a(t) = 3k and the initial velocity v(0) = 16i - 3j, we integrate the acceleration function with respect to time.
Integrating a(t) = 3k with respect to time gives us the velocity function v(t), considering the constant vector c for the integration:
v(t) = ∫ a(t) dt = ∫ 3k dt = 3kt + c
Using the initial condition v(0) = 16i - 3j, we find that:
c = 16i - 3j
Therefore, the velocity function is:
v(t) = 3kt + (16i - 3j)
This provides us with the correct expression for the velocity of the particle as a function of time.