Calculate the power of a crane in watts,which lifts a mass of $100 \, kg$ to a height of $10 \, m$ in $20 \, s$. (in $, W$)

$A$ 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 $\text{ W}$)

$A$ car of mass $2000 \ kg$ is accelerating from rest. If its engine is supplying a constant power of $10 \ kW$,then the velocity of the car at a time of $10 \ s$ is: (in $m \ s^{-1}$)

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

$A$ 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 engine develops $10 \text{ kW}$ of power. How much time will it take to lift a mass of $200 \text{ kg}$ to a height of $40 \text{ m}$? $(g = 10 \text{ m/s}^2)$