$($a$)$ A$$a$$daki $$st grafikte, $d=1$ boyutta $E$ toplam enerjill bir par$$a$$n$$n $(x,v)$ y$$r$$ngeleri g$$sterilmistir$.$ Alt grafi$$e$,$ bu y$$r$$ngeye sebep olan potanslyel enerji U yu ve toplam enerji E yl $$izin$.$ Not: $$st ve alt grafiklerin yatay ekseni aym$$dr$.$

$($b$)$st grafikte g$$sterilen y$$r$$ngeler saat y$$n$$nde mi$,$ saat$-$ters y$$n$$nde ml kat edilecektir? Cevabin$$z izah edin.

$($a$)$ In the top figure above, in $d=1,$ the $(x,v)$ 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 boyutta, $m$ kuitleli vhat$(x)$ hiz velt$$rlii bir pargacik,

$3$ m kiitleli' bir parcackla esnek carpuur. Carpum$$dan

sonra, $m$ k$$tleli parcacigm hiz vektor $u^{}{?}^{}-2$vhat$(x)$ dir.

$3$ m kithteli pareacigm, carpupmadan $$nce ve sonra hiz vekt$$riunii bulunuz.

In $d=1,$ 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 $-2v.$ Find the velocity, before and after the collision, of the particle with mass $3$ m $.$