An electric motor produces a tension of $4500 N$ in a wire and the reel winds at a rate of $2 ms^{-1}$. What is the power of the electric motor?

$A$ $10 \text{ H.P.}$ 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 ........... $\text{minutes}$ $(g = 10 \text{ m s}^{-2})$

$A$ force applied by an engine of a train of mass $2.05 \times 10^6 \; kg$ changes its velocity from $5 \; m/s$ to $25 \; m/s$ in $5$ minutes. The power of the engine is ........... $MW$.

An automobile engine of mass $m$ provides constant power $P$. The acceleration is given by $a = \frac{P}{mv}$. (Assume friction is absent). What is the distance covered by the vehicle while its velocity increases from $V_1$ to $V_2$?

$A$ body of mass $2 \text{ kg}$ begins to move under the influence of a time-dependent force $\vec{F} = (2t\hat{i} + 6t^2\hat{j}) \text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along the $x$ and $y$-axis respectively. The power produced by the force at $t = 2 \text{ s}$ is . . . . . . $\text{W}$.

If the maximum load carried by an elevator is $1400\,kg$ ($600\,kg$ passenger $+ 800\,kg$ elevator),which is moving up with a uniform speed of $3\,m/s$ and the frictional force acting on it is $2000\,N$,then the maximum power used by the motor is $...........\,kW$ (take $g = 10\,m/s^2$).