If a force $F$ is applied on a body and it moves with a velocity $v$,the power will be

$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $P$,then the position $s$ of the vehicle at time $t$ is given by:

An elevator in a building can carry a maximum of $10$ persons,with the average mass of each person being $68 \; kg$. The mass of the elevator itself is $920 \; kg$ and it moves with a constant speed of $3 \; m/s$. The frictional force opposing the motion is $6000 \; N$. If the elevator is moving up with its full capacity,the power delivered by the motor to the elevator $\left(g = 10 \; m/s^{2}\right)$ must be at least .............. $W$.

An engine pumps $100 \ kg$ of water to a height of $10 \ m$ in $5 \ s$. If the efficiency of the engine is $60\%$,the power of the engine is........$kW$. (Take $g = 10 \ m/s^2$.)

$A$ force applied by an engine on 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 (in $MW$)

$A$ body of mass $1 \ kg$ begins to move under the action of a time-dependent force $\vec{F} = (t \hat{i} + 2t^2 \hat{j}) \ N$,where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$ axes. The power developed by the above force at time $t = 3 \ s$ will be: (in $W$)