$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion?.......$cm$

$A$ body starting from rest at $t=0$ moves along a straight line with a constant acceleration. At $t=2 \ s$,the body reverses its direction keeping the acceleration same. The body returns to the initial position at $t=t_0$,then $t_0$ is

$A$ body of mass $4 \,kg$ is accelerated by a constant force. It travels a distance of $5 \,m$ in the first second and a distance of $2 \,m$ in the third second. The force acting on the body is: (in $\,N$)

The relation between position $(x)$ and time $(t)$ is given below for a particle moving along a straight line. Which of the following equations represents uniformly accelerated motion? [where $\alpha$ and $\beta$ are positive constants]

$A$ man of height $h$ is walking away from a street lamp with a constant speed $v$. The height of the street lamp is $3h$. The rate at which the length of the man's shadow is increasing when he is at a distance $10h$ from the base of the street lamp is:

If the velocity of a particle moving along the $x-$ axis is given by $v = k\sqrt{x}$,then which of the following is true? ($a$ is acceleration)