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

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 $Px=0PPx=\frac{b}{2}Pb=2m,c=\frac{5}{m}{x}^{}=4\frac{m}{s}0.$

$(b)$ 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 $x^{}=4\frac{m}{s}.$