An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

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

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?

The force required to row a boat at constant velocity is proportional to the square of its speed. If a speed of $v \, km/h$ requires $4 \, kW$ of power,how much power does a speed of $2v \, km/h$ require?

$A$ force of $(2\hat{i} + 3\hat{j} + 4\hat{k})\,N$ acts on a body for $4\,s$ and produces a displacement of $(3\hat{i} + 4\hat{j} + 5\hat{k})\,m$. The power used is :- ............... $W$ (in $.5$)

$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .