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 ........... $litres$.

Water is pumped from a depth of $10 \ m$ and delivered through a pipe of cross-section $10^{-2} \ m^2$. If it is needed to deliver a volume of $10^{-1} \ m^3$ per second,the power required will be ........ $kW$.

$A$ pump draws water from a tank which is $2.5\; m$ below the outlet and discharges it through a hose. The cross-sectional area of the hose is $10\; cm^{2}$,and the water leaves the end of the hose at a speed of $5\; m/s$. What is the power at which the pump is working (in $; W$)? (Assume $g = 10\; m/s^{2}$)

$A$ 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 $W$)

$A$ body is moving in a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to:

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point,driven with constant power $P$,is such that: