Two men have a weight ratio of $5 : 3$. If the ratio of the time taken by them to climb stairs is $11 : 9$,find the ratio of their power.

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?

$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $p$,what is the velocity of the vehicle at time $t$?

Water falls from a waterfall onto the blades of a turbine at a rate of $100 \ kg/s$. If the height of the fall is $100 \ m$,what is the power generated by the turbine?

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

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