Draw $x \to t$ graph for positive acceleration.

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x -$ axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration, $v =$ velocity, $x =$ displacement, $t =$ time)

Figure shows the position of a particle moving on the $x$-axis as a function of time

A bullet fired into a fixed target loses half of its velocity after penetrating $1\,cm.$ How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion

Which of the following speed-time $(v-t)$ graphs is physically not possible?

The velocity of the bullet becomes one third after it penetrates $4\,cm$ in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4+x)\,cm$ inside the block. The value of $x$ is$.....$