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

$A$ 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 $\text{ kW}$)

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:

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

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?

$A$ body of mass $4 \ kg$ is placed on a plane at a point $P$ having coordinates $(3, 4) \ m$. Under the action of force $\overrightarrow{F} = (2 \hat{i} + 3 \hat{j}) \ N$,it moves to a new point $Q$ having coordinates $(6, 10) \ m$ in $4 \ s$. The average power and instantaneous power at the end of $4 \ s$ are in the ratio of: