The velocity of a fluid particle moving along a horizontal streamline that coincides with the \(x\) axis in a plane, two-dimensional, incompressible flow field was experimentally found to be described by the equation \(u=x^{2}\). Along this streamline determine an expression for

(a) the rate of change of the \(v\) component of velocity with respect to \(y\),

(b) the acceleration of the particle,

(c) the pressure gradient in the \(x\) direction. The fluid is Newtonian.