At any instant of time $t$, the displacement of a particle is given by $x = 2t - 1$ ($SI$ units) under the influence of a force of $5 \,N$. The value of instantaneous power is (in $SI$ units):

$A$ man is riding a cycle with a velocity of $7.2 \text{ km/hr}$ up a hill having a slope of $1$ in $20$. The total mass of the man and the cycle is $100 \text{ kg}$. The power of the man is ............ $\text{W}$. (in $\text{ W}$)

$A$ 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 $..... \text{ W}$.

$A$ 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:

From a waterfall,water is falling down at the rate of $100 \ kg/s$ on the blades of a turbine. If the height of the fall is $100 \ m$,then the power delivered to the turbine is approximately equal to ........... $kW$.

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 $kW$)