$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $p$,what is the velocity of the vehicle at time $t$?

$A$ 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?

$A$ 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 $10 \; hours$?

$A$ body is moving along a straight line under the influence of a constant power source. If the relation between the displacement $(s)$ of the body and time $(t)$ is $s \propto t^x$, then $x=$

$A$ pump is used to deliver water at a certain rate from a given pipe. To obtain $n$ times the water in the same time from the same pipe,by what factor should the power of the motor be increased?

$A$ $10 \text{ H.P.}$ motor pumps out water from a well of depth $20 \text{ m}$ and fills a water tank of volume $22380 \text{ litres}$ at a height of $10 \text{ m}$ from the ground. The running time of the motor to fill the empty water tank is ........... $\text{minutes}$ $(g = 10 \text{ m s}^{-2})$