Assuming steady flow conditions, determine the following:

$($a$)$ What pressure gradient along the streamline, $\frac{dp}{ds},$ is required to accelerate water along a horizontal plane at a rate of $10m{s}^{-2}?$

$($b$)$ What pressure gradient is required to decelerate the same water at $20m{s}^{-2}?$

$($c$)$ Is the relationship between pressure gradient and fluid acceleration linear or nonlinear? Explain.