The power of a pump,which can pump $500 \,kg$ of water to a height of $100 \,m$ in $10 \,s$,is .......... $kW$. (Take $g = 10 \,m/s^2$)

$A$ box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to

An automobile of mass $m$ accelerates starting from the origin and is initially at rest,while the engine supplies constant power $P$. The position $x$ as a function of time $t$ is given by:

Water falls from a height of $60\, m$ at the rate of $15\, kg/s$ to operate a turbine. The losses due to frictional forces are $10\%$ of energy. How much power is generated by the turbine ............. $kW$ ? $(g = 10\, m/s^2)$

An automatic gun fires $360$ bullets per minute with a speed of $360 \,km/h$. If each bullet weighs $20 \,g$,the power of the gun is (in $\,W$)

The blades of a windmill sweep out a circle of area $A$.
$(a)$ If the wind flows at a velocity $v$ perpendicular to the circle,what is the mass of the air passing through it in time $t?$
$(b)$ What is the kinetic energy of the air?
$(c)$ Assume that the windmill converts $25\%$ of the wind's energy into electrical energy,and that $A=30\;m^{2}, v=36\;km/h$ and the density of air is $1.2\;kg\;m^{-3}.$ What is the electrical power produced?