$A$ body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 \sqrt{gh}$. The value of work done by the air friction is $.....$

$A$ block weighing $20 \ N$ travels down a smooth curved track $AB$ joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of $0.40$ with the block. If the block starts slipping on the track from a point $1.0 \ m$ above the horizontal surface,the distance it will move on the rough surface is: (in $m$)

$A$ body of mass $3 \text{ kg}$ is moving under the action of a force which causes a displacement of $\left(\frac{t^3}{3}\right) \text{ m}$, where '$t$' is time in seconds. The work done by the force in the first $2 \text{ seconds}$ is: (in $\text{ J}$)

$A$ bullet of mass $20 \,g$ leaves a rifle at an initial speed $100 \,m/s$ and strikes a target at the same level with speed $50 \,m/s$. The amount of work done by the resistance of air will be ......... $J$.

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

$A$ train engine of mass $m$ starts moving such that its velocity varies as $v = k\sqrt{s}$,where $k$ is a constant and $s$ is the distance covered. What is the total work done by all the forces acting on the engine in the first $t$ seconds?