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 $t \ge 0$.
$a(t) = (t, e^{-t}, 9)$, $(u_0, v_0, w_0) = (0, 0, 5)$, $(x_0, y_0, z_0) = (4, 0, 0)$
What is the velocity vector?
$v(t) = (?, ?, ?)$
What is the position vector?
$r(t) = (?, ?, ?)$