For the below accelerating flow $(U$ is a constant$),$ we want to find the velocity profile using the integral momentum approximation.

$($a$)(5$ Pts$)$ When $V_x$ is given as the following equations, show that $\frac{d}{dt}=6\frac{}{}$

$\frac{v_x}{U}=1-2\frac{y}{(t)}+(\frac{y}{(t)}{)}^2$ for $0y(t)$

$\frac{v_x}{U}=0$ for $y(t),((t)$: time $-$ dependent boundary layer thicknes $)$

$($b$)(3$ Pts$)$ Find $(t)$ by integrating the equation $(1)$ with respect to $t.$ Then, find the complete Vx by putting $(t)$ into the equation $(2).$

$($c$)(7$ Pts$)$To keep the velocity U as a constant, is the x $-$directional force imposed by the moving flat plate getting increased or decreased as time goes by$?$ At $t=3($s$),$ calculate the $x-$directional force when $U=0\mathrm{.}0001\frac{m}{s},={10}^{3}k\frac{g}{m^3},={10}^{-1}Pa*s,$ and the plate area is $10m^2.$