$A$ particle of mass $m$ slides down along a frictionless inclined plane $AC$ as shown in the figure. The kinetic energy of the particle at point $C$ is:

$A$ car accelerates from rest to $u \ m/s$. The energy spent in this process is $E \ J$. The energy required to accelerate the car from $u \ m/s$ to $2u \ m/s$ is $nE \ J$. The value of $n$ is ..............

$A$ $30 \, g$ bullet initially travelling at $120 \, m/s$ penetrates $12 \, cm$ into a wooden block. The average resistance force exerted by the wooden block is ........... $N$.

$A$ vertical spring with force constant $k$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

Consider an elliptically shaped rail $PQ$ in the vertical plane with $OP = 3 \ m$ and $OQ = 4 \ m$. $A$ block of mass $1 \ kg$ is pulled along the rail from $P$ to $Q$ with a force of $18 \ N$,which is always parallel to the line $PQ$ (see the figure). Assuming no frictional losses,the kinetic energy of the block when it reaches $Q$ is $(n \times 10) \ J$. The value of $n$ is (take acceleration due to gravity $g = 10 \ m/s^2$):

$A$ car moving with a velocity of $10 \, m/s$ can be stopped by the application of a constant force $F$ in a distance of $20 \, m$. If the velocity of the car is $30 \, m/s$,it can be stopped by this same force in what distance (in $, m$)?