$($a$)$ In the top figure above, in $\backslash (\backslash$mathrm$\{$d$\}=1\backslash ),$ the $\backslash ((\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$v$\})\backslash )$ trajectories of a particle with total energy E is shown. Draw, in the lower figure, the potential energy U and the total energy E causing these trajectories. The two figures have the same horizontal axis. $($b$)$ Are the trajectories shown in the top figure traversed in the clockwise or counterclockwise direction? Justify your answer.

$2.$

Bir boyntta, $\backslash ($ m $\backslash )$ kuthelic $\backslash ($ v $\backslash$hat$\{$x$\}\backslash )$ hiz veltoilii bir pargacik, $3$ m kitleli' bir pargacula emeh garphur. Carpusmadan sonra, $\backslash ($ m $\backslash )$ k$$tleli parsacigin haz vekt$$riu $\backslash (-2$ v $\backslash$hat$\{$x$\}\backslash )$ dir. $3$ m kiutleli pareacigm, carpurmadan $$nce ve sowra huz vektoriunic bulunuz.

In $\backslash (\backslash$mathrm$\{$d$\}=1\backslash ),$ a particle with mass m and velocity v elastically collides with a particle with mass $3$ m $.$ After the collision, the velocity of the particle with mass m is $-2$ v $.$ Find the velocity, before and after the collision, of the particle with mass $3$ m $.$