$A$ 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:

$A$ body of mass $4 \ kg$ is placed on a plane at a point $P$ having coordinates $(3, 4) \ m$. Under the action of force $\overrightarrow{F} = (2 \hat{i} + 3 \hat{j}) \ N$,it moves to a new point $Q$ having coordinates $(6, 10) \ m$ in $4 \ s$. The average power and instantaneous power at the end of $4 \ s$ are in the ratio of:

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

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

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

$A$ cylindrical well of radius $2.5 \ m$ has water up to a height of $14 \ m$ from the bottom. If the water level is at a depth of $6 \ m$ from the top of the well,then the time taken (in minutes) to empty the well using a motor of $10 \ HP$ is approximately,(Take $g = 10 \ m/s^2$)