$A$ 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 $kg$)

$A$ 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 ............... $\text{J/s}$.

Two men have a weight ratio of $5 : 3$. If the ratio of the time taken by them to climb stairs is $11 : 9$,find the ratio of their power.

$A$ body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement $s$ is given as a function of time $t$ as:

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

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 $100\, kg/m$. Calculate the power $W$ of the engine. (in $, W$)