$A$ man of mass $50 \ kg$ carries an object to a height of $20 \ m$ in a time of $10 \ s$. The power used by the man in this process is $2000 \ W$. Find the mass of the object carried by the man (take $g = 10 \ m/s^2$). (in $kg$)

The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10 \ g$ and the velocity of the bullets is $600 \ ms^{-1}$, the power (in $kW$) of the gun is

$A$ car of mass $1250 \ kg$ is moving with a velocity of $30 \ m/s$. If the engine delivers $30 \ kW$ of power and the resistive force acting on the car is $750 \ N$,find the maximum acceleration of the car.

$A$ body of mass $1\, kg$ begins to move under the action of a time-dependent force $\overrightarrow{F} = (2t\hat{i} + 3t^2\hat{j})\, N$,where $\hat{i}$ and $\hat{j}$ are unit vectors along the $x$ and $y$ axes. What power will be developed by the force at time $t$?

$A$ crane of efficiency $80 \%$ is used to lift $8000 \ kg$ of coal from a mine of depth $108 \ m$. If the time taken by the crane to lift the coal is one hour, then the power of the crane (in $kW$) is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

$A$ train of mass $2.05 \times 10^6 \ kg$ changes its velocity from $5 \ m/s$ to $25 \ m/s$ in $5 \ minutes$. The power of the engine is . . . . . . $MW$.