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 $, W$)

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{3t^2}{2} \, W$. Here,$t$ is in $s$. If the velocity of the particle at $t = 0$ is $v = 0$,the velocity of the particle at time $t = 2\, s$ will be ............ $m/s$.

$A$ pump on the ground floor of a building can pump up water to fill a tank of volume $30 \; m^{3}$ in $15 \; min$. If the tank is $40 \; m$ above the ground, and the efficiency of the pump is $30 \%$, how much electric power (in $kW$) is consumed by the pump?

$A$ $60 \ kg$ man runs up a staircase in $12 \ s$ while a $50 \ kg$ man runs up the same staircase in $11 \ s$. The ratio of the rate of doing their work is:

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. What is the power of the engine $?$ ................ $W$

$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .