$A$ body of mass $m$ accelerates uniformly from rest to $v_1$ in time $t_1$. As a function of time $t$,the instantaneous power delivered to the body is

The blades of a windmill sweep out a circle of area $A$.
$(a)$ If the wind flows at a velocity $v$ perpendicular to the circle,what is the mass of the air passing through it in time $t?$
$(b)$ What is the kinetic energy of the air?
$(c)$ Assume that the windmill converts $25\%$ of the wind's energy into electrical energy,and that $A=30\;m^{2}, v=36\;km/h$ and the density of air is $1.2\;kg\;m^{-3}.$ What is the electrical power produced?

Calculate the power of a crane in watts,which lifts a mass of $100 \, kg$ to a height of $10 \, m$ in $20 \, s$. (in $, W$)

$A$ 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 is moving along a straight line under the influence of a constant power source. If the relation between the displacement $(s)$ of the body and time $(t)$ is $s \propto t^x$, then $x=$

$A$ body is moving in a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to: