Suppose that the acceleration vector of a particle is given by a(t)=⟨−16cos(4t),−16sin(4t),−4t⟩, the paricle's initial velocity is v(0)=⟨1,0,1⟩, and the particle's initial position vector is r(0)=⟨1,1,1⟩. compute the following: a. the velocity vector of the particle at time t: v(t)= -4sin(4t)+1 i+ 4cos(4t)-4 j+ 4t^2/2-1 k b. the position vector of the particle at time t: r(t)= cos(4t)+t i+ sin4t-t+1 j+ 1 k