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 $\text{ W}$)

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point, driven with constant power $P$, is such that:

$A$ pump on the ground floor can pump up water to fill a tank of volume $30 \ m^3$ in $15 \ minutes$. If the tank is $40 \ m$ above the ground and the efficiency of the pump is $30\%$,then the electric power consumed by the pump is ....... $kW$.

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

$A$ $60 \ kg$ 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:

$A$ quarter horsepower motor runs at a speed of $600 \text{ r.p.m.}$ Assuming $40\%$ efficiency,the work done by the motor in one rotation will be: