$A$ 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 $W$)

The power of a pump,which can pump $200 \ kg$ of water to a height of $50 \ m$ in $10 \ s$,will be:

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 .............. $W$.

$A$ car of mass $1200 \,kg$ (together with the driver) is moving with a constant acceleration of $2 \,m/s^2$. How much power does the engine generate at the instant when the speed reaches $20 \,m/s$ (in $\,W$)? (Assume that the coefficient of friction between the car and the road is $0.5$ and $g = 10 \,m/s^2$).

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

$A$ force of $(2\hat i + 3\hat j + 4\hat k) \text{ N}$ acts on a body for $4 \text{ s}$ and produces a displacement of $(3\hat i + 4\hat j + 5\hat k) \text{ m}$. The power used is ............. $\text{W}$. (in $.5$)