When a constant force is applied to a body moving with constant acceleration,power does not remain constant. For power to be constant,the force has to vary with speed as follows:

$A$ water pump rated $600 W$ has an efficiency of $95 \%$. If it is used to raise water through a vertical distance of $60 m$,what is the volume of water drawn in $20$ minutes (in $m^3$)? [Use density of water $= 1000 kg/m^3$,$g = 10 m/s^2$]

$A$ man riding a bicycle moves at a speed of $7.2 \ km/hr$ up an incline having a length of $20 \ m$ and a height of $1 \ m$. The total mass of the man and the bicycle is $100 \ kg$. What is the power of the man in $W$?

$A$ body of mass $4 \ kg$ is placed on a plane at a point $P$ having coordinates $(3, 4) \ m$. Under the action of force $\overrightarrow{F} = (2 \hat{i} + 3 \hat{j}) \ N$,it moves to a new point $Q$ having coordinates $(6, 10) \ m$ in $4 \ s$. The average power and instantaneous power at the end of $4 \ s$ are in the ratio of:

$A$ body of mass $m$ starts from rest and is accelerated to a velocity $v$ in time $T$. The instantaneous power delivered to the body as a function of time $t$ is:

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