The power utilized when a force of $(2 \hat{i}+3 \hat{j}+4 \hat{k}) \text{ N}$ acts on a body for $4 \text{ s}$, producing a displacement of $(3 \hat{i}+4 \hat{j}+5 \hat{k}) \text{ m}$, is (in $\text{ W}$)

$A$ pump is used to lift $7200 \ kg$ of water per hour from a depth of $100 \ m$. Calculate the power of the pump in $kW$. Assume its efficiency is $50\%$.

$A$ tube-well pumps out $2400 \; kg$ of water per minute. If water is coming out with a velocity of $3 \; m/s$, how much work is done if the pump runs for $10 \; hours$?

$A$ pump is required to lift $1000 \, kg$ of water per minute from a well of depth $10 \, m$ and eject it with a speed of $10 \, m/s$. The horsepower of the engine needed is: (Assume $g = 10 \, m/s^2$)

$A$ body is moving unidirectionally under the influence of a constant power source. Its displacement in time $t$ is proportional to :

$A$ particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement $(s)$ - time $(t)$ graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale)