The power of a water pump is $4 \,kW$. If $g = 10 \,m/s^2$,the amount of water it can raise in $1 \,minute$ to a height of $20 \,m$ is ........... $litres$.

$A$ force applied by an engine of a train of mass $2.05 \times 10^6 \; kg$ changes its velocity from $5 \; m/s$ to $25 \; m/s$ in $5$ minutes. The power of the engine is ........... $MW$.

$A$ force of $(60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \text{ N}$ produces a velocity of $(2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \text{ m/s}$ in a particle. The value of power at that time will be: (in $\text{ W}$)

$A$ body of mass $1 \ kg$ begins to move under the action of a time-dependent force $\vec{F} = (t \hat{i} + 3t^2 \hat{j}) \ N$,where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axes. The power developed by the above force at time $t = 2 \ s$ will be $.............. \ W$.

$A$ car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

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?