$A$ 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 ..............

$A$ 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

State the importance of the work-energy theorem. Is the work-energy theorem a scalar or a vector?

$A$ car driver is trying to jump across a path as shown in the figure by driving horizontally off a cliff '$X$' at a speed of $10 \ m \ s^{-1}$. When he touches peak '$Z$' (ignore air resistance), what would be his speed (in $m \ s^{-1}$)? (use $g = 10 \ m \ s^{-2}$)

$A$ spring of force constant $k$ is fixed vertically on a table. $A$ ball of mass $m$ is dropped from a height $h$ onto the free end of the spring,causing the spring to compress by a distance $d$. What is the total work done in this process?

Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?