$A$ force acts on a body of mass $15 \,kg$, initially at rest. If the instantaneous power due to the force at the end of the third second is $5 \,W$, then the instantaneous power (in $W$) at the end of the $4 \,s$ will be

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

Which of the following must be known in order to determine the power output of an automobile?

$A$ 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 $\left(g=9.8 \,ms^{-2}\right)$.

Two men with weights in the ratio $4:3$ run up a staircase in time in the ratio $12:11$. The ratio of power of the first to that of second is

$A$ pump on the ground floor of a building can pump up water to fill a tank of volume $36 \,m^3$ in $30 \,min$. If the tank is $50 \,m$ above the ground, and the electric power consumed by the pump is $40 \,kW$, the efficiency of the pump is (Use $g=10 \,m / s^2$ and density of water $=1000 \,kg / m^3$ ) (in $\%$)