The Acceleration Vector For a Particle

The purpose of the following is to determine the acceleration of a particle over time in a flow field based on its 3 dimensional vector.

Image from the National Committee for Fluid Mechanics: Illustrate the Eulerian

Find the total Acceleration For Vector V:

V = 3ti + xzj + ty^2

Part 1 & Part 2

Find the partial derivatives (w.r.t. x, y ,z, & t) of the convective terms of the combined acceleration vector.

Part 3

Combine all four terms into the single , "total" or "substantial" derivative.