$A$ 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:

$A$ pump on the ground floor of a building can pump up water to fill a tank of volume $36 \,m^3$ in $30 \,min$. If the tank is $50 \,m$ above the ground, and the electric power consumed by the pump is $40 \,kW$, the efficiency of the pump is (Use $g=10 \,m / s^2$ and density of water $=1000 \,kg / m^3$ ) (in $\%$)

$A$ body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement $s$ is given as a function of time $t$ as:

The average power generated by a $90 \ kg$ mountain climber who climbs a summit of height $600 \ m$ in $90 \ minutes$ is (Acceleration due to gravity $= 10 \ ms^{-2}$). (in $W$)

$A$ 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 $W$)

$A$ man $M_1$ of mass $80 \ kg$ runs up the stairs with a box in $15 \ s$. Another man $M_2$ of the same mass $80 \ kg$ runs up the same stairs with the same box in $20 \ s$. Find the ratio of the power generated by them.