$A$ body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

$A$ 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 ............... $\text{J/s}$.

$A$ $10 \text{ H.P.}$ motor pumps out water from a well of depth $20 \text{ m}$ and fills a water tank of volume $22380 \text{ litres}$ at a height of $10 \text{ m}$ from the ground. The running time of the motor to fill the empty water tank is ........... $\text{minutes}$ $(g = 10 \text{ m s}^{-2})$

$A$ truck of mass $10,000 \ kg$ is moving up an inclined plane with a slope of $1 \ m$ in $50 \ m$. If the speed of the truck is $36 \ km/hr$,find the power of the engine in $kW$. (Take $g = 10 \ m/s^2$)

An elevator can carry a maximum load of $1800 \; kg$ (elevator $+$ passengers) and is moving up with a constant speed of $2 \; m s^{-1}$. The frictional force opposing the motion is $4000 \; N$. Determine the minimum power delivered by the motor to the elevator in watts as well as in horsepower.

$A$ crane of efficiency $80 \%$ is used to lift $8000 \ kg$ of coal from a mine of depth $108 \ m$. If the time taken by the crane to lift the coal is one hour, then the power of the crane (in $kW$) is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)