$A$ truck of mass $10,000 \ kg$ is moving up an inclined plane with a slope of $1 \ m$ in $50 \ m$. If the speed of the truck is $36 \ km/hr$,find the power of the engine in $kW$. (Take $g = 10 \ m/s^2$)

The average work done by a human heart while it beats once is $0.5 \, J$. Calculate the power used by the heart if it beats $72$ times in a minute.

$A$ body of mass $2 \text{ kg}$ begins to move under the influence of a time-dependent force $\vec{F} = (2t\hat{i} + 6t^2\hat{j}) \text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along the $x$ and $y$-axis respectively. The power produced by the force at $t = 2 \text{ s}$ is . . . . . . $\text{W}$.

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

$A$ girl of mass $50 \,kg$ is swinging on a cradle. If she moves with a velocity of $2 \,ms^{-1}$ in a direction making an angle of $60^{\circ}$ with the vertical, then the power generated by the gravitational force is $\left(g=9.8 \,ms^{-2}\right)$.

$A$ body of mass $m$ starts from rest and is accelerated uniformly to a velocity $v_1$ in time $t_1$. The instantaneous power delivered to the body as a function of time $t$ is: