What average horsepower is developed by an $80 \; kg$ man while climbing in $10 \; s$ a flight of stairs that rises $6 \; m$ vertically?

An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

$A$ body of mass $m$ is initially at rest. It is subjected to a uniform acceleration such that it acquires a velocity $v$ in time $T$. The instantaneous power supplied to the body as a function of time $t$ is . . . . . . .

$A$ motor boat is moving in a river with velocity $\vec{v} = 7 \hat{i} + 2 \hat{j} - 5 \hat{k} \text{ m/s}$. If the flow of water offers a resistive force $\vec{F} = 9 \hat{i} + 3 \hat{j} - 3 \hat{k} \text{ N}$, then the power of the boat is: (in $\text{ W}$)

$A$ constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{3t^2}{2} \, W$. Here,$t$ is in $s$. If the velocity of the particle at $t = 0$ is $v = 0$,the velocity of the particle at time $t = 2\, s$ will be ............ $m/s$.