A particle, constrained to move along the $x-$axis, has a total mechanical energy of $-100$ J $.$ The potential energy of the particle is shown in the graph. At time $t=0,$ the particle is located at $x=5\mathrm{.}5cm$ and is moving to the left. $($a$)$ What is the particle's potential energy at $t=0?$ What is its kinetic energy at this time? $($b$)$ What are the particle's total, potential, and kinetic energies when it is at $x=1cm$ and moving to the right? $($c$)$ What is the particle's kinetic energy when it is at $x=3cm$ and moving to the left?

$($d$)$ Describe the motion of this particle starting at $t=0.$