$A$ motor boat is travelling with a speed of $3.0\, m/s$. If the force on it due to water flow is $500\, N$,the power of the boat is

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 pump lifts $6$ tonnes of water from a well of depth $25 \ m$ to the first floor of height $35 \ m$ from the ground floor in $20$ minutes. The power of the pump (in $kW$) is: $[g=10 \ ms^{-2}]$

$A$ 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 $W$?

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. Calculate the power $W$ of the engine. (in $, W$)

$A$ force $\vec{F} = (4 \hat{i} + \hat{j} - 2 \hat{k}) \text{ N}$ acting on a body maintains its velocity at $\vec{v} = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \text{ m s}^{-1}$. The power exerted is $..... \text{ W}$.