The force required to row a boat at constant velocity is proportional to the square of its speed. If a speed of $v \, km/h$ requires $4 \, kW$ of power,how much power does a speed of $2v \, km/h$ require?

$A$ 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 $\text{ kW}$)

$A$ 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 $t$?

$A$ 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 . . . . . . .

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 $W$)

An engine is dragging a mass of $5000 \ kg$ with a velocity of $5 \ ms^{-1}$ along a smooth inclined plane of inclination $1$ in $50$. Then the power of the engine is (in $kW$)