$A$ motor can pump $7560 \text{ kg}$ of water per hour from a well of depth $100 \text{ m}$. If the efficiency of the pump is $70 \%$, then the power of the pump is (Acceleration due to gravity $= 10 \text{ m s}^{-2}$) (in $\text{ kW}$)

$A$ body of mass $2 \ kg$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $P$. Its displacement in $4 \ s$ is $\frac{1}{3} \alpha^2 \sqrt{P} \ m$. The value of $\alpha$ will be $.............$

An object of mass $m$ is projected with an initial velocity $u$ at an angle $\theta$ with the horizontal. What is the average power delivered by gravity in reaching the highest point?

$A$ body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by

$A$ 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 $10 \; hours$?

$A$ 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)