Air strikes the blades of a windmill with a speed of $v$. The power generated is proportional to which of the following?

$A$ body of mass $2 \ kg$ begins to move under the action of a time-dependent force given by $\overrightarrow{F} = (6t \hat{i} + 6t^2 \hat{j}) \ N$. The power developed by the force at time $t$ is given by:

Power of a water pump is $2 \, kW$. If $g = 10 \, m/s^2$,the amount of water it can raise in one minute to a height of $10 \, m$ is .............. $liter$.

$A$ pump is used to lift $7200 \ kg$ of water per hour from a depth of $100 \ m$. Calculate the power of the pump in $kW$. Assume its efficiency is $50\%$.

$A$ body of mass $2 \,kg$ starts from rest and moves with uniform acceleration. It acquires a velocity $20 \,ms^{-1}$ in $4 \,s$. The power exerted on the body in $2 \,s$ in watts is

$A$ motor can pump $7560 \text{ kg}$ of water per hour from a well of depth $100 \text{ m}$. If the efficiency of the pump is $70 \%$, then the power of the pump is (Acceleration due to gravity $= 10 \text{ m s}^{-2}$) (in $\text{ kW}$)