How to find 3D position function given acceleration (worked example)

An example problem involving position, velocity and acceleration in 3-Space is worked algebraically, numerically (with MATLAB) and graphically (CaclPlot3D). Here is the example problem:

A mathematical bug is flying through 3-space. We only have a few pieces of information about this bug’s motion. We know that at all points in time the bug’s acceleration vector is a =〈6t,2,12t〉 and we know that v=〈4, 2, 11〉 and we know that at time t=−1 the bug is located at the point (−3, 4,−7). Find the bug’s location at time t=3.