$A$ force $\vec{F} = (4 \hat{i} + \hat{j} - 2 \hat{k}) \text{ N}$ acting on a body maintains its velocity at $\vec{v} = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \text{ m s}^{-1}$. The power exerted is $..... \text{ W}$.

$A$ $10 \text{ H.P.}$ 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 ........... $\text{minutes}$ $(g = 10 \text{ m s}^{-2})$

$A$ car of mass $m$ has an engine which can deliver power $P$. The minimum time in which the car can be accelerated from rest to a speed $v$ is .............

$A$ 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 engine pumps $100 \ kg$ of water to a height of $10 \ m$ in $5 \ s$. If the efficiency of the engine is $60\%$,the power of the engine is........$kW$. (Take $g = 10 \ m/s^2$.)

$A$ body of mass $m$ accelerates uniformly from rest to $v_1$ in time $t_1$. As a function of time $t$,the instantaneous power delivered to the body is