$A$ 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 $\text{ kW}$)

$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{3t^2}{2} \, W$. Here,$t$ is in $s$. If the velocity of the particle at $t = 0$ is $v = 0$,the velocity of the particle at time $t = 2\, s$ will be ............ $m/s$.

$A$ 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 $t$?

The power of a water pump is $4 \,kW$. If $g = 10 \,m/s^2$,the amount of water it can raise in $1 \,minute$ to a height of $20 \,m$ is ........... $litres$.

If the maximum load carried by an elevator is $1400\,kg$ ($600\,kg$ passenger $+ 800\,kg$ elevator),which is moving up with a uniform speed of $3\,m/s$ and the frictional force acting on it is $2000\,N$,then the maximum power used by the motor is $...........\,kW$ (take $g = 10\,m/s^2$).