Problem H$\mathrm{.}1.$A

Given: A particle P travels on a path described by the Cartesian coordinates of $y=cx(b-x),$ where $x$ and $y$ have the units of meters. The $x-$component of velocity, $x^{},$ for P is constant.

Find: For this problem:

$($a$)$ Make a sketch of the path of P over the range of $x=0x=\frac{b}{2}b=2m,c=\frac{5}{m}{x}^{}=4\frac{m}{s}0.$

$(b)$ Determine the Cartesian components $of$ the velocity and acceleration $ofPatx=0.$ Add a sketch $of$ the velocity and acceleration vectors for $Pto$ your path drawn above.

$(c)$ Determine the Cartesian components $of$ the velocity and acceleration $ofPatx=\frac{b}{2.}$ Add a sketch $of$ the velocity and acceleration vectors for $Pto$ your path drawn above.

Use the following parameters $in$ your analysis: $b=2m,c=\frac{5}{m}$ and $x^{}=4\frac{m}{s}.$

Make a short concise sentence for the given and find statements as well.