A particle of mass m moves on the surface z = f(x, y). Let x = x(t) and y = y(t) be the x- and y-coordinates of the particle at time t.

(a) Find the velocity vector v and the kinetic energy K = 1/2m|v|² of the particle. 

(b) Determine the acceleration vector a. 

(c) Let z = x² + y² and x(t) = t cos t, y(t) = t sin t. Find the velocity vector, the kinetic energy, and the acceleration vector.