$A$ car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

The power of a pump,which can pump $200 \ kg$ of water to a height of $200 \ m$ in $10 \ s$,is ................ $kW$ $(g = 10 \ m/s^2)$.

$A$ force acts on a body of mass $15 \,kg$, initially at rest. If the instantaneous power due to the force at the end of the third second is $5 \,W$, then the instantaneous power (in $W$) at the end of the $4 \,s$ will be

$A$ 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 . . . . . . .

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 $g = 10\,m/s^2$).

$A$ pump is used to lift $7200 \ kg$ of water per hour from a depth of $100 \ m$. Calculate the power of the pump in $kW$. Assume its efficiency is $50\%$.