Not exactly homework in my case but I guess it fits the level. We know that a = v dv/dx holds when moving on a line. Does it hold when moving on a plane? If yes, what would be the exact formulation of the statement. I mean, I read a = v dv/dx as a(x) = v(x) dv/dx(x) (or are they functions of t?) but since on a plane a(x), v(x) and dv/dx(x) are all vectors, how do we define the product?